Difference between revisions of "Applications-of-GeoGebra/C2/Conic-Sections-Hyperbola/English"

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(Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''Conic Sections - Hyperbola''' |- | | ''...")
 
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−
 
 
{|border=1
 
{|border=1
−
| | '''Visual Cue'''
+
||'''Visual Cue'''
−
| | '''Narration'''
+
||'''Narration'''
  
 
|-
 
|-
−
| | '''Slide Number 1'''
+
||'''Slide Number 1'''
  
 
'''Title Slide'''
 
'''Title Slide'''
−
| | Welcome to this tutorial on '''Conic Sections - Hyperbola'''
+
||Welcome to this tutorial on '''Conic Sections - Hyperbola'''.
 
|-
 
|-
−
| | '''Slide Number 2'''
+
||'''Slide Number 2'''
  
 
'''Learning Objectives'''
 
'''Learning Objectives'''
−
| | In this tutorial, we will:
+
||In this tutorial, we will:
  
 
Study standard equations and parts of hyperbolae
 
Study standard equations and parts of hyperbolae
  
−
Learn how to use '''GeoGebra''' to construct a hyperbola
+
Learn how to use '''GeoGebra''' to construct a hyperbola.
 
|-
 
|-
−
| | '''Slide Number 3'''
+
||'''Slide Number 3'''
  
 
'''System Requirement'''
 
'''System Requirement'''
−
| | Here I am using:
+
||Here I am using:
  
 
'''Ubuntu Linux OS''' version 14.04
 
'''Ubuntu Linux OS''' version 14.04
Line 28: Line 27:
 
'''GeoGebra 5.0.388.0-d'''
 
'''GeoGebra 5.0.388.0-d'''
 
|-
 
|-
−
| | '''Slide Number 4'''
+
||'''Slide Number 4'''
  
 
'''Pre-requisites'''
 
'''Pre-requisites'''
−
 
−
 
−
 
−
 
−
 
  
 
'''www.spoken-tutorial.org'''
 
'''www.spoken-tutorial.org'''
−
| | To follow this tutorial, you should be familiar with
+
||To follow this tutorial, you should be familiar with
  
 
'''GeoGebra''' interface
 
'''GeoGebra''' interface
Line 46: Line 40:
 
For relevant tutorials, please visit our website.
 
For relevant tutorials, please visit our website.
 
|-
 
|-
−
| | '''Slide Number 5'''
+
||'''Slide Number 5'''
  
 
'''Hyperbola'''
 
'''Hyperbola'''
Line 55: Line 49:
  
 
A hyperbola is the locus of points whose difference of distances from these foci is constant.
 
A hyperbola is the locus of points whose difference of distances from these foci is constant.
−
| | Consider two fixed points '''F1''' and '''F2''' called foci.
+
||Hyperbola,
 +
 
 +
Consider two fixed points '''F1''' and '''F2''' called foci.
  
 
A hyperbola is the locus of points whose difference of distances from these foci is constant.
 
A hyperbola is the locus of points whose difference of distances from these foci is constant.
  
−
In the image, observe that foci of a hyperbola lie along the transverse axis.''' '''
+
In the image, observe that foci of a hyperbola lie along the transverse axis.
  
 
They are equidistant from the center which lies on the conjugate axis.
 
They are equidistant from the center which lies on the conjugate axis.
Line 69: Line 65:
 
The conjugate axis is perpendicular to the transverse axis.
 
The conjugate axis is perpendicular to the transverse axis.
  
−
The hyperbola intersects the transverse axis at the vertices''' A '''and''' B'''.
+
The hyperbola intersects the transverse axis at the vertices '''A ''' and '''B'''.
  
 
'''a''' is the distance of each vertex from the center.
 
'''a''' is the distance of each vertex from the center.
Line 77: Line 73:
 
They are perpendicular to the transverse axis.
 
They are perpendicular to the transverse axis.
 
|-
 
|-
−
| |
+
||
−
| | Be careful to distinguish lengths from letters used for '''sliders''', circles and hyperbolae.
+
||Be careful to distinguish lengths from letters used for '''sliders''', circles and hyperbolae.
 
|-
 
|-
−
| | Show the '''GeoGebra''' window.
+
||Show the '''GeoGebra''' window.
−
| | Let us construct a hyperbola in '''GeoGebra'''.
+
||Let us construct a hyperbola in '''GeoGebra'''.
  
 
I have already opened the '''GeoGebra''' interface.
 
I have already opened the '''GeoGebra''' interface.
 
|-
 
|-
−
| | Click on '''Point''' tool and click twice in '''Graphics''' view.
+
||Click on '''Point''' tool >> click twice in '''Graphics''' view.
  
 
Point to '''A''' and '''B'''.
 
Point to '''A''' and '''B'''.
−
| | Click on '''Point''' tool and click twice in '''Graphics''' view.
+
||Click on '''Point''' tool and click twice in '''Graphics''' view.
  
 
This creates two points ''' A''' and '''B''', which will be the foci of our hyperbola.
 
This creates two points ''' A''' and '''B''', which will be the foci of our hyperbola.
 
|-
 
|-
−
| | Right-click on '''A''' and choose '''Rename''' option.
+
||Right-click on '''A''' >> choose '''Rename''' option.
−
| | Right-click on '''A''' and choose the '''Rename''' option.
+
||Right-click on '''A''' and choose the '''Rename''' option.
 
|-
 
|-
−
| | Type '''F1''' in the '''New Name''' field >> click '''OK '''button.
+
||Type '''F1''' in the '''New Name''' field >> click '''OK '''button.
−
| | In the '''New Name''' field, type '''F1''' and click '''OK'''.
+
||In the '''New Name''' field, type '''F1''' and click '''OK'''.
 
|-
 
|-
−
| | This will be one of our foci, '''F1'''.
+
||Point to the focus '''F1'''.
−
| | This will be one of our foci, '''F1'''.
+
||This will be one of our foci, '''F1'''.
 
|-
 
|-
−
| |
+
||Point to '''B'''.
−
| | Let us rename point''' B''' as '''F2'''.
+
||Let us rename point '''B''' as '''F2'''.
 
|-
 
|-
−
| | Click on '''Slider''' tool >> click in '''Graphics '''view.
+
||Click on '''Slider''' tool >> click in '''Graphics '''view.
−
| | Click on '''Slider''' tool and click in '''Graphics '''view.
+
||Click on '''Slider''' tool and click in '''Graphics '''view.
 
|-
 
|-
−
| | Point to the ''' Slider dialog box''' in '''Graphics''' view.
+
||Point to the '''Slider dialog box''' in '''Graphics''' view.
−
| | A '''Slider dialog-box''' appears in '''Graphics''' view.
+
||A '''Slider dialog-box''' appears in '''Graphics''' view.
 
|-
 
|-
−
| | Stay with the default '''Number''' radio-button selection.
+
||Stay with the default '''Number''' radio-button selection.
  
 
In the '''Name''' field, type '''k'''.
 
In the '''Name''' field, type '''k'''.
−
| | Stay with the default '''Number''' selection.
+
||Stay with the default '''Number''' selection.
  
 
In the '''Name''' field, type '''k'''.
 
In the '''Name''' field, type '''k'''.
 
|-
 
|-
−
| | Set '''Min''' value as 0, '''Max''' value as 10, '''increment''' as 0.1, click '''OK'''.
+
||Set '''Min''' value as 0, '''Max''' value as 10, '''increment''' as 0.1, click '''OK'''.
−
| | Set '''Min''' value as 0, '''Max''' value as 10, '''increment''' as 0.1, click '''OK'''.
+
||Set '''Min''' value as 0, '''Max''' value as 10, '''increment''' as 0.1, click '''OK'''.
 
|-
 
|-
−
| | Point to '''slider k'''.
+
||Point to '''slider k'''.
−
| | This creates a number '''slider''' named '''k'''.
+
||This creates a number '''slider''' named '''k'''.
 
|-
 
|-
−
| | Drag the '''slider k''' from 1 to 10.
+
||Drag the '''slider k''' from 1 to 10.
−
| | Using this '''slider''', '''k''' can be changed from 0 to 10.
+
||Using this '''slider''', '''k''' can be changed from 0 to 10.
 
|-
 
|-
−
| | Point to''' slider k'''.
+
||Point to '''slider k'''.
−
| | '''k''' will be the difference of the distances of any point on the hyperbola from the foci, '''F1''' and '''F2'''.
+
||'''k''' will be the difference of the distances of any point on the hyperbola from the foci, '''F1''' and '''F2'''.
 
|-
 
|-
−
| | Drag '''slider k''' to 4.
+
||Drag '''slider k''' to 4.
−
| | Drag '''slider k''' to 4.
+
||Drag '''slider k''' to 4.
 
|-
 
|-
−
| |
+
||
−
| | We will create another '''number slider''' named “'''a'''”.
+
||We will create another '''number slider''' named '''a'''.
 
|-
 
|-
−
| | Point to '''slider a'''.
+
||Point to '''slider a'''.
−
| | Its '''Min''' value is 0, '''Max''' value is 25,'''increment''' is 0.1.
+
||Its '''Min''' value is 0, '''Max''' value is 25,'''increment''' is 0.1.
 
|-
 
|-
−
| | Click on '''Circle with Center and Radius''' tool >> click on '''F1'''.
+
||Click on '''Circle with Center and Radius''' tool >> click on '''F1'''.
−
| | Click on '''Circle with Center and Radius''' tool and click on '''F1'''.
+
||Click on '''Circle with Center and Radius''' tool and click on '''F1'''.
 
|-
 
|-
−
| | Point to '''text box'''; type '''a''' and click '''OK'''.
+
||Point to '''text box'''; type '''a''' >> click '''OK'''.
−
| | A '''text-box''' appears; type '''a''' and click '''OK'''.
+
||A '''text-box''' appears; type '''a''' and click '''OK'''.
 
|-
 
|-
−
| | Drag '''a''' to a value between 2 and 3.
+
||Drag '''a''' to a value between 2 and 3.
−
| | Drag '''a''' to a value between 2 and 3.
+
||Drag '''a''' to a value between 2 and 3.
 
|-
 
|-
−
| | Point to the circle '''c''' with center '''F1''' and '''radius a'''.
+
||Point to the circle '''c''' with center '''F1''' and '''radius a'''.
−
| | A circle '''c''' with center '''F1''' and radius '''a''' appears.
+
||A circle '''c''' with center '''F1''' and radius '''a''' appears.
 
|-
 
|-
−
| | Drag '''slider a''' to 5.
+
||Drag '''slider a''' to 5.
−
| | Drag '''slider a''' to 5.
+
||Drag '''slider a''' to 5.
 
|-
 
|-
−
| | Under '''Move Graphics View''', click on '''Zoom Out''' tool.
+
||Under '''Move Graphics View''', click on '''Zoom Out''' tool.
−
| | Under '''Move Graphics View''', click on '''Zoom Out''' tool.
+
||Under '''Move Graphics View''', click on '''Zoom Out''' tool.
 
|-
 
|-
−
| | Click in '''Graphics''' view.
+
||Click in '''Graphics''' view.
−
| | Click twice in '''Graphics''' view.
+
||Click in '''Graphics''' view.
 
|-
 
|-
−
| | Click on '''Move Graphics View''' tool to move the background.
+
||Click on '''Move Graphics View''' tool to move the background.
−
| | Click on '''Move Graphics View''' to move the background as required.
+
||Click on '''Move Graphics View''' to move the background as required.
 
|-
 
|-
−
| | Click again on '''Circle with Center and Radius''' tool.
+
||Click again on '''Circle with Center and Radius''' tool.
  
 
Click on '''F2'''.
 
Click on '''F2'''.
−
| | Click again on '''Circle with Center and Radius''' tool and click on ''' F2'''.
+
||Click again on '''Circle with Center and Radius''' tool and click on ''' F2'''.
 
|-
 
|-
−
| | Point to the '''text-box'''; type '''a-k''' and click '''OK'''.
+
||Point to the '''text-box'''; type '''a-k''' >> click '''OK'''.
−
| | In the '''text-box''', type '''a minus k''' and click '''OK'''.
+
||In the '''text-box''', type '''a minus k''' and click '''OK'''.
 
|-
 
|-
−
| | Point to the circle '''d''' with center '''F2''' and radius '''a-k'''.
+
||Point to the circle '''d''' with center '''F2''' and radius '''a-k'''.
−
| | Circle '''d''' with center '''F2''' and radius '''a minus k''' appears.
+
||Circle '''d''' with center '''F2''' and radius '''a minus k''' appears.
 
|-
 
|-
−
| | Click again on '''Circle with Center and Radius''' tool.
+
||Click on '''Circle with Center and Radius''' tool.
  
 
Click on '''F2'''.
 
Click on '''F2'''.
−
| | Click again on '''Circle with Center and Radius''' tool and click on '''F2'''.
+
||Click again on '''Circle with Center and Radius''' tool and click on '''F2'''.
 
|-
 
|-
−
| | Point to the '''text box'''; type '''a+k''' and click '''OK'''.
+
||Point to the '''text box'''; type '''a+k''' >> click '''OK'''.
−
| | In the '''text-box''', type '''a plus k''' and click '''OK'''.
+
||In the '''text-box''', type '''a plus k''' and click '''OK'''.
 
|-
 
|-
−
| | Point to the circle '''e''' with center '''F2''' and '''radius a+k'''.
+
||Point to the circle '''e''' with center '''F2''' and '''radius a+k'''.
−
| | Circle '''e''' with center '''F2''' and radius '''a plus k''' appears.
+
||Circle '''e''' with center '''F2''' and radius '''a plus k''' appears.
 
|-
 
|-
−
| | Set '''slider k''' between 1 and 2, '''slider a''' between 3 and 4.
+
||Set '''slider k''' between 1 and 2, '''slider a''' between 3 and 4.
−
| | Set '''slider k''' between 1 and 2, '''slider a''' between 3 and 4.
+
||Set '''slider k''' between 1 and 2, '''slider a''' between 3 and 4.
 
|-
 
|-
−
| | Click on '''Intersect''' tool under '''Point''' tool.
+
||Click on '''Intersect''' tool under '''Point''' tool.
  
 
Click on circles '''c'''and '''d'''and circles '''c'''and '''e'''.
 
Click on circles '''c'''and '''d'''and circles '''c'''and '''e'''.
−
| | Under '''Point''', click on '''Intersect'''.
+
||Under '''Point''', click on '''Intersect'''.
  
 
Then click on circles '''c''' and '''d''' and circles '''c''' and '''e'''.
 
Then click on circles '''c''' and '''d''' and circles '''c''' and '''e'''.
 
|-
 
|-
−
| | Point to points '''A''', '''B''', '''C''' and '''D'''.
+
||Point to points '''A''', '''B''', '''C''' and '''D'''.
−
| | This creates points '''A''', '''B''', '''C''' and '''D'''.
+
||This creates points '''A''', '''B''', '''C''' and '''D'''.
 
|-
 
|-
−
| | Under '''Line''' tool, click on '''Segment''' tool >> click on points '''A''' and '''F1'''
+
||Under '''Line''' tool, click on '''Segment''' tool >> click on points '''A''' and '''F1'''
  
 
Click on points '''A''' and '''F2.'''
 
Click on points '''A''' and '''F2.'''
−
| | Under '''Line''', click on '''Segment''' and click on points '''A''' and '''F1''' to join them.
+
||Under '''Line''', click on '''Segment''' and click on points '''A''' and '''F1''' to join them.
  
 
Then click on points '''A''' and '''F2''' to join them.
 
Then click on points '''A''' and '''F2''' to join them.
 
|-
 
|-
−
| | Click on Segment tool >> join the points B and F1 >> join B and F2.
+
||Click on Segment tool >> join the points B and F1 >> join B and F2.
−
| | Similarly, using '''Segment''' tool, join '''B''' and '''F1''' as well as '''B''' and '''F2'''.
+
||Similarly, using '''Segment''' tool, join '''B''' and '''F1''' as well as '''B''' and '''F2'''.
 
|-
 
|-
−
| | Click on '''Move''' tool.
+
||Click on '''Move''' tool.
−
| | Click on '''Move'''.
+
||Click on '''Move'''.
 
|-
 
|-
−
| | Double click on segment '''AF1''' >> '''Object Properties'''.
+
||Double click on segment '''AF1''' >> '''Object Properties'''.
−
| | Double click on segment '''AF1''' and click on '''Object Properties'''.
+
||Double click on segment '''AF1''' and click on '''Object Properties'''.
 
|-
 
|-
−
| | Point to the left panel and to highlighted segment '''AF1'''.
+
||Point to the left panel and to highlighted segment '''AF1'''.
−
| | In the left panel, segment '''AF1''' is already highlighted.
+
||In the left panel, segment '''AF1''' is already highlighted.
 
|-
 
|-
−
| | Holding '''Ctrl''' Key down, click and highlight segments '''AF2, BF1''' and '''BF2'''.
+
||Holding '''Ctrl''' Key down, click and highlight segments '''AF2, BF1''' and '''BF2'''.
−
| | Holding '''Ctrl''' Key down, click and highlight segments '''AF2, BF1''' and '''BF2'''.
+
||Holding '''Ctrl''' Key down, click and highlight segments '''AF2, BF1''' and '''BF2'''.
 
|-
 
|-
−
| | Under '''Basic''' tab, make sure '''Show Label''' is checked.
+
||Under '''Basic''' tab, make sure '''Show Label''' is checked.
−
| | Under the '''Basic''' tab, make sure '''Show Label''' is checked.
+
||Under the '''Basic''' tab, make sure '''Show Label''' is checked.
 
|-
 
|-
−
| | Choose '''Name and Value''' from the dropdown menu next to it.
+
||Choose '''Name and Value''' from the dropdown menu next to it.
−
| | Choose '''Name and Value''' from the dropdown menu next to it.
+
||Choose '''Name and Value''' from the dropdown menu next to it.
 
|-
 
|-
−
| | Under '''Color''' tab, select red.
+
||Under '''Color''' tab, select red.
−
| | Under the '''Color''' tab, select red.
+
||Under the '''Color''' tab, select red.
 
|-
 
|-
−
| | Under '''Style''' tab, select '''dashed line style'''.
+
||Under '''Style''' tab, select '''dashed line style'''.
−
| | Under the '''Style''' tab, select '''dashed line style'''.
+
||Under the '''Style''' tab, select '''dashed line style'''.
 
|-
 
|-
−
| | Close '''Preferences''' box.
+
||Close '''Preferences''' box.
−
| | Close the '''Preferences''' box.
+
||Close the '''Preferences''' box.
 
|-
 
|-
−
| | Click on '''Move''' tool >> move the labels properly in '''Graphics''' view.
+
||Click on '''Move''' tool >> move the labels properly in '''Graphics''' view.
−
| | Click on '''Move''' if it is not highlighted.
+
||Click on '''Move''' if it is not highlighted.
  
 
Move the labels to see them properly in '''Graphics''' view.
 
Move the labels to see them properly in '''Graphics''' view.
 
|-
 
|-
−
| |
+
||
−
| | Now, let us carry out the same steps for segments '''CF1''', '''CF2''', '''DF1''' and '''DF2''' but make them blue.
+
||Now, let us carry out the same steps for segments '''CF1''', '''CF2''', '''DF1''' and '''DF2''' but make them blue.
 
|-
 
|-
−
| | Click on '''Move''' tool >> move the labels properly in '''Graphics''' view.
+
||Click on '''Move''' tool >> move the labels properly in '''Graphics''' view.
−
| | Click on '''Move''' if it is not highlighted.
+
||Click on '''Move''' if it is not highlighted.
  
 
And move the labels to see them properly in '''Graphics''' view.
 
And move the labels to see them properly in '''Graphics''' view.
 
|-
 
|-
−
| | Right-click on points '''A, B, C''' and '''D''' and select '''Trace On''' option.
+
||Right-click on points '''A, B, C''' and '''D''' >> select '''Trace On''' option.
−
| | Right-click on points '''A, B, C''' and '''D''' and select '''Trace On''' option.
+
||Right-click on points '''A, B, C''' and '''D''' and select '''Trace On''' option.
 
|-
 
|-
−
| | Set '''slider k''' at 1.
+
||Set '''slider k''' at 1.
  
 
Drag '''slider a''' to both ends of '''slider'''.
 
Drag '''slider a''' to both ends of '''slider'''.
−
| | Set '''slider k''' at 1.
+
||Set '''slider k''' at 1.
  
 
Drag '''slider a''' to both ends of the '''slider'''.
 
Drag '''slider a''' to both ends of the '''slider'''.
  
−
Set
 
 
|-
 
|-
−
| | Set '''slider k''' at 2 and drag '''slider a''' to both ends.
+
||Set '''slider k''' at 2 and drag '''slider a''' to both ends.
−
| | First '''k''' at 2.
+
||First '''k''' at 2.
 
|-
 
|-
−
| | Set '''slider k''' at 3 and drag '''slider a''' to both ends.
+
||Set '''slider k''' at 3 and drag '''slider a''' to both ends.
−
| | Then at 3.
+
||Then at 3.
 
|-
 
|-
−
| | Set '''slider k''' at 5 and drag '''slider a''' again to both ends.
+
||Set '''slider k''' at 5 and drag '''slider a''' again to both ends.
−
| | At 5.
+
||At 5.
 
|-
 
|-
−
| | Set '''slider k''' at 10 and drag '''slider a''' yet again to both ends.
+
||Set '''slider k''' at 10 and drag '''slider a''' yet again to both ends.
−
| | And finally at 10.
+
||And finally at 10.
 
|-
 
|-
−
| | Point to the traces of hyperbolae for different values of '''a''' and '''k'''.
+
||Point to the traces of hyperbolae for different values of '''a''' and '''k'''.
−
| | Observe the traces of hyperbolae for the different values of '''a''' and '''k'''.
+
||Observe the traces of hyperbolae for the different values of '''a''' and '''k'''.
 
|-
 
|-
−
| |
+
||
−
| | Let us look at the equations of hyperbolae.
+
||Let us look at the equations of hyperbolae.
 
|-
 
|-
−
| | In the '''input bar''', type '''(x-h)^2/a^2-(y-k)^2/b^2=1''' and press '''Enter'''.
+
||In the '''input bar''', type '''(x-h)^2/a^2-(y-k)^2/b^2=1''' and press '''Enter'''.
  
 
To type the '''caret symbol''', hold the '''Shift''' key down and press 6.
 
To type the '''caret symbol''', hold the '''Shift''' key down and press 6.
−
| | Open a new '''GeoGebra''' window.
+
||Open a new '''GeoGebra''' window.
  
 
In the '''input bar''', type the following line describing the difference of two fractions equal to 1.
 
In the '''input bar''', type the following line describing the difference of two fractions equal to 1.
Line 288: Line 283:
  
  
−
For the 1<sup>st</sup> '''fraction''', type the '''numerator''' as '''x minus h in parentheses caret 2'''.
+
For the 1<sup>st</sup> fraction, type the numerator as '''x minus h''' in parentheses '''caret 2'''.
  
 +
Then type division slash.
  
−
Then type '''division slash'''.
+
Now, type the denominator of the 1<sup>st</sup> fraction as '''a caret 2''' followed by '''minus'''.
  
 +
For the 2<sup>nd</sup> fraction, type the numerator as '''y minus k''' in parentheses '''caret 2'''.
  
−
Now, type the '''denominator''' of the 1<sup>st</sup> '''fraction''' as '''a caret 2''' followed by '''minus'''.
+
Then type division slash.
−
 
+
−
 
+
−
For the 2<sup>nd</sup> fraction, type the '''numerator''' as '''y minus k in parentheses caret 2'''.
+
−
 
+
−
 
+
−
Then type '''division slash'''.
+
−
 
+
−
 
+
−
Now, type the '''denominator''' of the 2<sup>nd</sup> '''fraction''' as '''b caret 2''' followed by '''equals sign 1'''.
+
  
 +
Now, type the denominator of the 2<sup>nd</sup> fraction as '''b caret 2''' followed by '''equals sign 1'''. 
  
 
Press '''Enter'''.
 
Press '''Enter'''.
 
|-
 
|-
−
| | Point to the popup window.
+
||Point to the popup window.
−
| | A pop-up window asks if you want to create '''sliders''' for '''a, b, h''' and '''k'''.
+
||A pop-up window asks if you want to create '''sliders''' for '''a, b, h''' and '''k'''.
 
|-
 
|-
−
| | Click on '''Create Sliders'''.
+
||Click on '''Create Sliders'''.
−
| | Click on '''Create Sliders'''.
+
||Click on '''Create Sliders'''.
 
|-
 
|-
−
| | Point to '''sliders a, b, h''' and '''k'''.
+
||Point to '''sliders a, b, h''' and '''k'''.
−
| | This creates number '''sliders''' for '''h, a, k''' and ''' b'''.
+
||This creates number '''sliders''' for '''h, a, k''' and ''' b'''.
 
|-
 
|-
−
| | Double-click on the '''sliders''' to see their properties.
+
||Double-click on the '''sliders''' to see their properties.
−
| | By default, they go from minus 5 to 5 and are set at 1.
+
||By default, they go from minus 5 to 5 and are set at 1.
  
 
You can double-click on the '''sliders''' to see their properties.
 
You can double-click on the '''sliders''' to see their properties.
 
|-
 
|-
−
| | Point to the hyperbola in '''Graphics''' view.
+
||Point to the hyperbola in '''Graphics''' view.
−
| | A hyperbola appears in '''Graphics''' view.
+
||A hyperbola appears in '''Graphics''' view.
 
|-
 
|-
−
| | Under '''Move Graphics View''', click on '''Zoom Out''' tool and then in '''Graphics '''view.
+
||Under '''Move Graphics View''', click on '''Zoom Out''' tool >> click in '''Graphics '''view.
−
| | Under '''Move Graphics View''', click on '''Zoom Out''' and then in '''Graphics '''view.
+
||Under '''Move Graphics View''', click on '''Zoom Out''' and then in '''Graphics '''view.
 
|-
 
|-
−
| | Click on '''Move Graphics View''' and drag '''Graphics''' view to see hyperbola properly.
+
||Click on '''Move Graphics View''' >> drag '''Graphics''' view to see hyperbola properly.
−
| | Click on '''Move Graphics View''' and drag '''Graphics''' view to see the hyperbola properly.
+
||Click on '''Move Graphics View''' and drag '''Graphics''' view to see the hyperbola properly.
 
|-
 
|-
−
| | Point to the equation for hyperbola '''c''' in '''Algebra''' view.
+
||Point to the equation for hyperbola '''c''' in '''Algebra''' view.
−
| | In '''Algebra''' view, note the equation for hyperbola '''c'''.
+
||In '''Algebra''' view, note the equation for hyperbola '''c'''.
 
|-
 
|-
−
| | Drag boundary to left of '''Slider '''tool see equation properly.
+
||Drag boundary to left of '''Slider '''tool see equation properly.
−
| | Drag the boundary to see it properly.
+
||Drag the boundary to see it properly.
 
|-
 
|-
−
| | Point to the equations appearing in '''Algebra''' view.
+
||Point to the equations appearing in '''Algebra''' view.
−
| | Keep track of the equations appearing in '''Algebra''' view as you the drag the '''sliders''' from end to end.
+
||Keep track of the equations appearing in '''Algebra''' view as you the drag the '''sliders''' from end to end.
 
|-
 
|-
−
| | Point to hyperbola '''c'''.
+
||Point to hyperbola '''c'''.
−
| | You will see the effects on the shape of hyperbola '''c'''.
+
||You will see the effects on the shape of hyperbola '''c'''.
 
|-
 
|-
−
| | Place the cursor over the equation in '''Algebra''' view.
+
||Place the cursor over the equation in '''Algebra''' view.
−
| | Place the cursor over the equation in '''Algebra''' view.
+
||Place the cursor over the equation in '''Algebra''' view.
 
|-
 
|-
−
| | Point to '''slider a''' and hyperbola '''c'''.
+
||Point to '''slider a''' and hyperbola '''c'''.
  
 
Drag '''slider a'''.
 
Drag '''slider a'''.
−
| | Note that '''a''' is associated with the '''x minus h squared''' component of the equation.
+
||Note that '''a''' is associated with the '''x minus h squared''' component of the equation.
  
 
It controls the horizontal movement of hyperbola '''c'''.
 
It controls the horizontal movement of hyperbola '''c'''.
 
|-
 
|-
−
| | Point to '''slider b''' and hyperbola '''c'''.
+
||Point to '''slider b''' and hyperbola '''c'''.
  
 
Drag '''slider b'''.
 
Drag '''slider b'''.
−
| | Associated with the '''y minus k squared''' component is '''b'''.
+
||Associated with the '''y minus k squared''' component is '''b'''.
  
 
It controls the vertical movement of hyperbola '''c'''.
 
It controls the vertical movement of hyperbola '''c'''.
 
|-
 
|-
−
| | Point to hyperbola '''c'''.
+
||Point to hyperbola '''c'''.
−
| | Note that the '''transverse axis''' of hyperbola '''c''' is horizontal like the '''x axis.'''
+
||Note that the '''transverse axis''' of hyperbola '''c''' is horizontal like the '''x axis'''.
 
|-
 
|-
−
| | Drag '''slider a''' to 2, leaving '''b''' at 1.
+
||Drag '''slider a''' to 2, leaving '''b''' at 1.
−
| | Drag '''slider a''' to 2, leaving '''b''' at 1.
+
||Drag '''slider a''' to 2, leaving '''b''' at 1.
 
|-
 
|-
−
| | Point to hyperbola '''c'''.
+
||Point to hyperbola '''c'''.
−
| | When '''a''' is greater than '''b''', the arms of the hyperbola are closer to the '''x axis'''.
+
||When '''a''' is greater than '''b''', the arms of the hyperbola are closer to the '''x axis'''.
 
|-
 
|-
−
| | Point to equation of hyperbola '''c'''.
+
||Point to equation of hyperbola '''c'''.
−
| | Note the equation of the hyperbola.
+
||Note the equation of the hyperbola.
 
|-
 
|-
−
| | Drag boundary to see it properly.
+
||Drag boundary to see it properly.
−
| | Drag the boundary to see it properly.
+
||Drag the boundary to see it properly.
 
|-
 
|-
−
| | Point to '''slider''' at 2.
+
||Point to '''slider''' at 2.
  
 
Drag '''slider b''' to 3.
 
Drag '''slider b''' to 3.
−
| | With '''slider a''' at 2, drag '''slider b''' to 3.
+
||With '''slider a''' at 2, drag '''slider b''' to 3.
 
|-
 
|-
−
| | Point to '''sliders a''' and '''b''', and hyperbola '''c'''.
+
||Point to '''sliders a''' and '''b''', and hyperbola '''c'''.
−
| | When '''a''' is less than '''b''', the arms of the hyperbola stretch closer to the '''y axis'''.
+
||When '''a''' is less than '''b''', the arms of the hyperbola stretch closer to the '''y axis'''.
 
|-
 
|-
−
| | Point to '''equation''' of hyperbola '''c'''.
+
||Point to '''equation''' of hyperbola '''c'''.
−
| | Note the equation of hyperbola '''c'''.
+
||Note the equation of hyperbola '''c'''.
 
|-
 
|-
−
| | Drag boundary to see it properly.
+
||Drag boundary to see it properly.
−
| | Drag the boundary to see it properly.
+
||Drag the boundary to see it properly.
 
|-
 
|-
−
| | With '''slider a''' at 2, drag '''slider b''' to 1.
+
||With '''slider a''' at 2, drag '''slider b''' to 1.
−
| | With '''slider a''' at 2, drag '''slider b''' back to 1.
+
||With '''slider a''' at 2, drag '''slider b''' back to 1.
 
|-
 
|-
−
| | Click in and drag '''Graphics''' view to see hyperbola properly.
+
||Click in and drag '''Graphics''' view to see hyperbola properly.
−
| | Click in and drag '''Graphics''' view to see the hyperbola properly.
+
||Click in and drag '''Graphics''' view to see the hyperbola properly.
 
|-
 
|-
−
| | Type '''Focus(c)''' in the '''input bar''' >> press '''Enter'''.
+
||Type '''Focus(c)''' in the '''input bar''' >> press '''Enter'''.
−
| | In the '''input bar''', type '''Focus c in parentheses''' and press '''Enter'''.
+
||In the '''input bar''', type '''Focus c''' in parentheses and press '''Enter'''.
 
|-
 
|-
−
| | Point to '''A''' and '''B''' in '''Graphics '''view'''.'''
+
||Point to '''A''' and '''B''' in '''Graphics '''view'''.'''
  
 
Point to the '''co-ordinates''' in '''Algebra''' view.
 
Point to the '''co-ordinates''' in '''Algebra''' view.
−
| | Two foci,''' A''' and '''B''', are mapped in '''Graphics''' view.
+
||Two foci,''' A''' and '''B''', are mapped in '''Graphics''' view.
  
 
Their '''coordinates''' appear in '''Algebra''' view.
 
Their '''coordinates''' appear in '''Algebra''' view.
 
|-
 
|-
−
| | Type '''Center(c)''' in the '''input bar''' and press '''Enter'''.
+
||Type '''Center(c)''' in the '''input bar''' and press '''Enter'''.
−
| | In the '''input bar''', type '''Center c in parentheses''' and press '''Enter'''.
+
||In the '''input bar''', type '''Center c''' in parentheses and press '''Enter'''.
 
|-
 
|-
−
| | Point to point '''C''' in '''Graphics''' view
+
||Point to point '''C''' in '''Graphics''' view
  
 
Point the '''co-ordinates''' in '''Algebra''' view.
 
Point the '''co-ordinates''' in '''Algebra''' view.
−
| | Center, point '''C''', appears in '''Graphics''' view.
+
||Center, point '''C''', appears in '''Graphics''' view.
  
−
Its '''co-ordinates''' appear in '''Algebra''' view.
+
Its co-ordinates appear in '''Algebra''' view.
 
|-
 
|-
−
| | Point to the '''co-ordinates''' '''(h, k)''' of center '''C''' in '''Algebra''' view.
+
||Point to the co-ordinates '''(h, k)''' of center '''C''' in '''Algebra''' view.
−
| | Note that the center has the '''coordinates h comma k'''.
+
||Note that the center has the coordinates '''h comma k'''.
 
|-
 
|-
−
| | Drag '''sliders h''' and '''k''' from end to end.
+
||Drag '''sliders h''' and '''k''' from end to end.
−
| | Drag '''sliders h''' and '''k''' from end to end.
+
||Drag '''sliders h''' and '''k''' from end to end.
 
|-
 
|-
−
| | Point to hyperbola '''c'''.
+
||Point to hyperbola '''c'''.
−
| | Note the effects on hyperbola '''c'''.
+
||Note the effects on hyperbola '''c'''.
 
|-
 
|-
−
| | Type '''Vertex(c)''' in the '''input bar''' >> press '''Enter'''.
+
||Type '''Vertex(c)''' in the '''input bar''' >> press '''Enter'''.
−
| | In the '''input bar''', type '''Vertex c in parentheses''' and press '''Enter'''.
+
||In the '''input bar''', type '''Vertex c''' in parentheses and press '''Enter'''.
 
|-
 
|-
−
| | Point to '''D''' and '''E'''.
+
||Point to '''D''' and '''E'''.
  
−
 
+
Drag '''slider a''' to ~0.5 so we can see the vertices clearly.
−
 
+
||Vertices, '''D''' and '''E''', appear on hyperbola '''c'''.
−
 
+
−
Let us drag '''slider a''' to ~0.5 so we can see the vertices clearly.
+
−
| | Vertices, '''D''' and '''E''', appear on hyperbola '''c'''.
+
  
 
Let us drag '''slider a''' so we can see the vertices clearly.
 
Let us drag '''slider a''' so we can see the vertices clearly.
 
|-
 
|-
−
| | Drag boundary to see '''Graphics''' view properly.
+
||Drag boundary to see '''Graphics''' view properly.
−
| | Drag the boundary to see '''Graphics''' view properly.
+
||Drag the boundary to see '''Graphics''' view properly.
 
|-
 
|-
−
| | Click in and drag '''Graphics''' view to see hyperbola.
+
||Click in and drag '''Graphics''' view to see hyperbola.
−
| | Click in '''Graphics''' view and drag the background so you can see the hyperbola properly.
+
||Click in '''Graphics''' view and drag the background so you can see the hyperbola properly.
 
|-
 
|-
−
| | Drag '''slider a''' back to 2.
+
||Drag '''slider a''' back to 2.
−
| | Drag '''slider a''' back to 2.
+
||Drag '''slider a''' back to 2.
 
|-
 
|-
−
| | Click on '''Text''' tool under '''Slider''' tool and click in '''Graphics''' view.
+
||Click on '''Text''' tool under '''Slider''' tool >> click in '''Graphics''' view.
−
| | Under '''Slider''', click on '''Text''' and click in '''Graphics''' view.
+
||Under '''Slider''', click on '''Text''' and click in '''Graphics''' view.
 
|-
 
|-
−
| | Point to the '''text box'''.
+
||Point to the '''text box'''.
  
 
In '''Edit''' field, type the following '''text'''.
 
In '''Edit''' field, type the following '''text'''.
−
| | A text-box opens up.
+
||A text-box opens up.
  
 
In the '''Edit''' field, type the following text.
 
In the '''Edit''' field, type the following text.
 
|-
 
|-
−
| | Show '''Slide Number 6'''.
+
||'''Slide Number 6'''.
−
| | Press '''Enter''' after each line to go to the next line.
+
−
 
+
−
Click '''OK'''.
+
−
|-
+
−
| | '''Slide Number 6'''
+
  
−
'''Text box for hyperbola c'''
+
'''Text box for Hyperbola c'''
  
−
transverse axis 2a = 4
+
Transverse axis 2a = 4
  
 
c = 2.24
 
c = 2.24
  
−
conjugate axis 2b = 2.018
+
Conjugate axis 2b = 2.018
  
 
e = 1.12
 
e = 1.12
  
 
latus rectum = 1.018
 
latus rectum = 1.018
−
| | '''Text box for hyperbola c'''
+
||Press '''Enter''' after each line to go to the next line and
  
−
transverse axis '''2a''' equals 4
+
Click '''OK'''.
−
 
+
−
'''c''' equals 2.24
+
−
 
+
−
conjugate axis '''2b''' equals 2.018
+
−
 
+
−
'''e''' equals 1.12
+
−
 
+
−
latus rectum equals 1.018
+
 
|-
 
|-
−
| |
+
||
−
| | Refer to '''additional material''' providedwith this '''tutorial''' for these calculations.
+
||Refer to '''additional material''' provided with this '''tutorial''' for these calculations.
 
|-
 
|-
−
| | Click on '''Move Graphics View''' and drag the background so you can see the hyperbola.
+
||Click on '''Move Graphics View''' and drag the background to see the hyperbola.
−
| | Click on '''Move Graphics View''' and drag the background so you can see the hyperbola.
+
||Click on '''Move Graphics View''' and drag the background so you can see the hyperbola.
 
|-
 
|-
−
| | Uncheck equation '''c''' and all points and text generated for hyperbola '''c''' in '''Algebra''' view.
+
||Uncheck equation '''c''' and all points and text generated for hyperbola '''c''' in '''Algebra''' view.
−
| | Uncheck equation '''c''' and all points and text generated for '''hyperbola c''' in '''Algebra''' view.
+
||Uncheck equation '''c''' and all points and text generated for '''hyperbola c''' in '''Algebra''' view.
 
|-
 
|-
−
| | Show screenshots of hyperbola '''d''' for '''a=2, b=1''' and '''a=2, b=3'''.
+
||Show screenshots of hyperbola '''d''' for '''a=2, b=1''' and '''a=2, b=3'''.
−
| | Follow the earlier steps to construct hyperbola '''d''' for these two conditions.
+
||Follow the earlier steps to construct hyperbola '''d''' for these two conditions.
 
|-
 
|-
−
| |
+
||
−
| | Let us summarize.
+
||Let us summarize.
 
|-
 
|-
−
| | '''Slide Number 8'''
+
||'''Slide Number 8'''
  
 
'''Summary'''
 
'''Summary'''
−
| | In this tutorial, we have learnt how to use '''GeoGebra''' to:
+
||In this tutorial, we have learnt how to use '''GeoGebra''' to:
  
 
Construct a hyperbola
 
Construct a hyperbola
Line 510: Line 483:
 
Look at standard equations and parts of hyperbolae
 
Look at standard equations and parts of hyperbolae
 
|-
 
|-
−
| | '''Slide Number 9'''
+
||'''Slide Number 9'''
  
 
'''Assignment'''
 
'''Assignment'''
Line 523: Line 496:
  
 
Calculate eccentricity and length of latus recti, transverse and conjugate axes.
 
Calculate eccentricity and length of latus recti, transverse and conjugate axes.
−
| | As an '''assignment,'''
+
||As an assignment,  
−
 
+
−
Construct hyperbolae with the following foci and vertices.
+
  
 
Find all these values.
 
Find all these values.
 
|-
 
|-
−
| | '''Slide Number 10'''
+
||'''Slide Number 10'''
  
 
'''Assignment'''
 
'''Assignment'''
Line 540: Line 511:
  
 
'''49y<sup>2</sup> – 16x<sup>2</sup> = 784'''
 
'''49y<sup>2</sup> – 16x<sup>2</sup> = 784'''
−
| | Find all these values for these hyperbolae.
+
||Find all these values for these hyperbolae.
 
|-
 
|-
−
| | '''Slide Number 11'''
+
||'''Slide Number 11'''
  
 
'''About Spoken Tutorial project'''
 
'''About Spoken Tutorial project'''
−
| | The video at the following link summarizes the Spoken Tutorial project.
+
||The video at the following link summarizes the Spoken Tutorial project.
  
 
Please download and watch it.
 
Please download and watch it.
 
|-
 
|-
−
| | '''Slide Number 12'''
+
||'''Slide Number 12'''
  
 
'''Spoken Tutorial workshops'''
 
'''Spoken Tutorial workshops'''
−
| | The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.
+
||The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.
  
 
For more details, please write to us.
 
For more details, please write to us.
 
|-
 
|-
−
| | '''Slide Number 13'''
+
||'''Slide Number 13'''
  
 
'''Forum for specific questions:'''
 
'''Forum for specific questions:'''
Line 569: Line 540:
  
 
Someone from our team will answer them.
 
Someone from our team will answer them.
−
| | Please post your timed queries on this forum.
+
||Please post your timed queries on this forum.
 
|-
 
|-
−
| | '''Slide Number 14'''
+
||'''Slide Number 14'''
  
 
'''Acknowledgement'''
 
'''Acknowledgement'''
−
| | '''Spoken Tutorial Project '''is funded by NMEICT, MHRD, Government of India.
+
||'''Spoken Tutorial Project''' is funded by NMEICT, MHRD, Government of India.
  
 
More information on this mission is available at this link.
 
More information on this mission is available at this link.
 
|-
 
|-
−
| |
+
||
−
| | This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.
+
||This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.
  
 
Thank you for joining.
 
Thank you for joining.
 
|-
 
|-
 
|}
 
|}

Revision as of 12:34, 31 August 2018

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this tutorial on Conic Sections - Hyperbola.
Slide Number 2

Learning Objectives

In this tutorial, we will:

Study standard equations and parts of hyperbolae

Learn how to use GeoGebra to construct a hyperbola.

Slide Number 3

System Requirement

Here I am using:

Ubuntu Linux OS version 14.04

GeoGebra 5.0.388.0-d

Slide Number 4

Pre-requisites

www.spoken-tutorial.org

To follow this tutorial, you should be familiar with

GeoGebra interface

Conic Sections in geometry

For relevant tutorials, please visit our website.

Slide Number 5

Hyperbola

[[Image:]]

Consider two fixed points F1and F2 called foci.

A hyperbola is the locus of points whose difference of distances from these foci is constant.

Hyperbola,

Consider two fixed points F1 and F2 called foci.

A hyperbola is the locus of points whose difference of distances from these foci is constant.

In the image, observe that foci of a hyperbola lie along the transverse axis.

They are equidistant from the center which lies on the conjugate axis.

2b is the length of the conjugate axis.

c is the distance of each focus from the center.

The conjugate axis is perpendicular to the transverse axis.

The hyperbola intersects the transverse axis at the vertices A and B.

a is the distance of each vertex from the center.

The latus recti pass through the foci.

They are perpendicular to the transverse axis.

Be careful to distinguish lengths from letters used for sliders, circles and hyperbolae.
Show the GeoGebra window. Let us construct a hyperbola in GeoGebra.

I have already opened the GeoGebra interface.

Click on Point tool >> click twice in Graphics view.

Point to A and B.

Click on Point tool and click twice in Graphics view.

This creates two points A and B, which will be the foci of our hyperbola.

Right-click on A >> choose Rename option. Right-click on A and choose the Rename option.
Type F1 in the New Name field >> click OK button. In the New Name field, type F1 and click OK.
Point to the focus F1. This will be one of our foci, F1.
Point to B. Let us rename point B as F2.
Click on Slider tool >> click in Graphics view. Click on Slider tool and click in Graphics view.
Point to the Slider dialog box in Graphics view. A Slider dialog-box appears in Graphics view.
Stay with the default Number radio-button selection.

In the Name field, type k.

Stay with the default Number selection.

In the Name field, type k.

Set Min value as 0, Max value as 10, increment as 0.1, click OK. Set Min value as 0, Max value as 10, increment as 0.1, click OK.
Point to slider k. This creates a number slider named k.
Drag the slider k from 1 to 10. Using this slider, k can be changed from 0 to 10.
Point to slider k. k will be the difference of the distances of any point on the hyperbola from the foci, F1 and F2.
Drag slider k to 4. Drag slider k to 4.
We will create another number slider named a.
Point to slider a. Its Min value is 0, Max value is 25,increment is 0.1.
Click on Circle with Center and Radius tool >> click on F1. Click on Circle with Center and Radius tool and click on F1.
Point to text box; type a >> click OK. A text-box appears; type a and click OK.
Drag a to a value between 2 and 3. Drag a to a value between 2 and 3.
Point to the circle c with center F1 and radius a. A circle c with center F1 and radius a appears.
Drag slider a to 5. Drag slider a to 5.
Under Move Graphics View, click on Zoom Out tool. Under Move Graphics View, click on Zoom Out tool.
Click in Graphics view. Click in Graphics view.
Click on Move Graphics View tool to move the background. Click on Move Graphics View to move the background as required.
Click again on Circle with Center and Radius tool.

Click on F2.

Click again on Circle with Center and Radius tool and click on F2.
Point to the text-box; type a-k >> click OK. In the text-box, type a minus k and click OK.
Point to the circle d with center F2 and radius a-k. Circle d with center F2 and radius a minus k appears.
Click on Circle with Center and Radius tool.

Click on F2.

Click again on Circle with Center and Radius tool and click on F2.
Point to the text box; type a+k >> click OK. In the text-box, type a plus k and click OK.
Point to the circle e with center F2 and radius a+k. Circle e with center F2 and radius a plus k appears.
Set slider k between 1 and 2, slider a between 3 and 4. Set slider k between 1 and 2, slider a between 3 and 4.
Click on Intersect tool under Point tool.

Click on circles cand dand circles cand e.

Under Point, click on Intersect.

Then click on circles c and d and circles c and e.

Point to points A, B, C and D. This creates points A, B, C and D.
Under Line tool, click on Segment tool >> click on points A and F1

Click on points A and F2.

Under Line, click on Segment and click on points A and F1 to join them.

Then click on points A and F2 to join them.

Click on Segment tool >> join the points B and F1 >> join B and F2. Similarly, using Segment tool, join B and F1 as well as B and F2.
Click on Move tool. Click on Move.
Double click on segment AF1 >> Object Properties. Double click on segment AF1 and click on Object Properties.
Point to the left panel and to highlighted segment AF1. In the left panel, segment AF1 is already highlighted.
Holding Ctrl Key down, click and highlight segments AF2, BF1 and BF2. Holding Ctrl Key down, click and highlight segments AF2, BF1 and BF2.
Under Basic tab, make sure Show Label is checked. Under the Basic tab, make sure Show Label is checked.
Choose Name and Value from the dropdown menu next to it. Choose Name and Value from the dropdown menu next to it.
Under Color tab, select red. Under the Color tab, select red.
Under Style tab, select dashed line style. Under the Style tab, select dashed line style.
Close Preferences box. Close the Preferences box.
Click on Move tool >> move the labels properly in Graphics view. Click on Move if it is not highlighted.

Move the labels to see them properly in Graphics view.

Now, let us carry out the same steps for segments CF1, CF2, DF1 and DF2 but make them blue.
Click on Move tool >> move the labels properly in Graphics view. Click on Move if it is not highlighted.

And move the labels to see them properly in Graphics view.

Right-click on points A, B, C and D >> select Trace On option. Right-click on points A, B, C and D and select Trace On option.
Set slider k at 1.

Drag slider a to both ends of slider.

Set slider k at 1.

Drag slider a to both ends of the slider.

Set slider k at 2 and drag slider a to both ends. First k at 2.
Set slider k at 3 and drag slider a to both ends. Then at 3.
Set slider k at 5 and drag slider a again to both ends. At 5.
Set slider k at 10 and drag slider a yet again to both ends. And finally at 10.
Point to the traces of hyperbolae for different values of a and k. Observe the traces of hyperbolae for the different values of a and k.
Let us look at the equations of hyperbolae.
In the input bar, type (x-h)^2/a^2-(y-k)^2/b^2=1 and press Enter.

To type the caret symbol, hold the Shift key down and press 6.

Open a new GeoGebra window.

In the input bar, type the following line describing the difference of two fractions equal to 1.


To type the caret symbol, hold the Shift key down and press 6.


For the 1st fraction, type the numerator as x minus h in parentheses caret 2.

Then type division slash.

Now, type the denominator of the 1st fraction as a caret 2 followed by minus.

For the 2nd fraction, type the numerator as y minus k in parentheses caret 2.

Then type division slash.

Now, type the denominator of the 2nd fraction as b caret 2 followed by equals sign 1.

Press Enter.

Point to the popup window. A pop-up window asks if you want to create sliders for a, b, h and k.
Click on Create Sliders. Click on Create Sliders.
Point to sliders a, b, h and k. This creates number sliders for h, a, k and b.
Double-click on the sliders to see their properties. By default, they go from minus 5 to 5 and are set at 1.

You can double-click on the sliders to see their properties.

Point to the hyperbola in Graphics view. A hyperbola appears in Graphics view.
Under Move Graphics View, click on Zoom Out tool >> click in Graphics view. Under Move Graphics View, click on Zoom Out and then in Graphics view.
Click on Move Graphics View >> drag Graphics view to see hyperbola properly. Click on Move Graphics View and drag Graphics view to see the hyperbola properly.
Point to the equation for hyperbola c in Algebra view. In Algebra view, note the equation for hyperbola c.
Drag boundary to left of Slider tool see equation properly. Drag the boundary to see it properly.
Point to the equations appearing in Algebra view. Keep track of the equations appearing in Algebra view as you the drag the sliders from end to end.
Point to hyperbola c. You will see the effects on the shape of hyperbola c.
Place the cursor over the equation in Algebra view. Place the cursor over the equation in Algebra view.
Point to slider a and hyperbola c.

Drag slider a.

Note that a is associated with the x minus h squared component of the equation.

It controls the horizontal movement of hyperbola c.

Point to slider b and hyperbola c.

Drag slider b.

Associated with the y minus k squared component is b.

It controls the vertical movement of hyperbola c.

Point to hyperbola c. Note that the transverse axis of hyperbola c is horizontal like the x axis.
Drag slider a to 2, leaving b at 1. Drag slider a to 2, leaving b at 1.
Point to hyperbola c. When a is greater than b, the arms of the hyperbola are closer to the x axis.
Point to equation of hyperbola c. Note the equation of the hyperbola.
Drag boundary to see it properly. Drag the boundary to see it properly.
Point to slider at 2.

Drag slider b to 3.

With slider a at 2, drag slider b to 3.
Point to sliders a and b, and hyperbola c. When a is less than b, the arms of the hyperbola stretch closer to the y axis.
Point to equation of hyperbola c. Note the equation of hyperbola c.
Drag boundary to see it properly. Drag the boundary to see it properly.
With slider a at 2, drag slider b to 1. With slider a at 2, drag slider b back to 1.
Click in and drag Graphics view to see hyperbola properly. Click in and drag Graphics view to see the hyperbola properly.
Type Focus(c) in the input bar >> press Enter. In the input bar, type Focus c in parentheses and press Enter.
Point to A and B in Graphics view.

Point to the co-ordinates in Algebra view.

Two foci, A and B, are mapped in Graphics view.

Their coordinates appear in Algebra view.

Type Center(c) in the input bar and press Enter. In the input bar, type Center c in parentheses and press Enter.
Point to point C in Graphics view

Point the co-ordinates in Algebra view.

Center, point C, appears in Graphics view.

Its co-ordinates appear in Algebra view.

Point to the co-ordinates (h, k) of center C in Algebra view. Note that the center has the coordinates h comma k.
Drag sliders h and k from end to end. Drag sliders h and k from end to end.
Point to hyperbola c. Note the effects on hyperbola c.
Type Vertex(c) in the input bar >> press Enter. In the input bar, type Vertex c in parentheses and press Enter.
Point to D and E.

Drag slider a to ~0.5 so we can see the vertices clearly.

Vertices, D and E, appear on hyperbola c.

Let us drag slider a so we can see the vertices clearly.

Drag boundary to see Graphics view properly. Drag the boundary to see Graphics view properly.
Click in and drag Graphics view to see hyperbola. Click in Graphics view and drag the background so you can see the hyperbola properly.
Drag slider a back to 2. Drag slider a back to 2.
Click on Text tool under Slider tool >> click in Graphics view. Under Slider, click on Text and click in Graphics view.
Point to the text box.

In Edit field, type the following text.

A text-box opens up.

In the Edit field, type the following text.

Slide Number 6.

Text box for Hyperbola c

Transverse axis 2a = 4

c = 2.24

Conjugate axis 2b = 2.018

e = 1.12

latus rectum = 1.018

Press Enter after each line to go to the next line and

Click OK.

Refer to additional material provided with this tutorial for these calculations.
Click on Move Graphics View and drag the background to see the hyperbola. Click on Move Graphics View and drag the background so you can see the hyperbola.
Uncheck equation c and all points and text generated for hyperbola c in Algebra view. Uncheck equation c and all points and text generated for hyperbola c in Algebra view.
Show screenshots of hyperbola d for a=2, b=1 and a=2, b=3. Follow the earlier steps to construct hyperbola d for these two conditions.
Let us summarize.
Slide Number 8

Summary

In this tutorial, we have learnt how to use GeoGebra to:

Construct a hyperbola

Look at standard equations and parts of hyperbolae

Slide Number 9

Assignment

Construct hyperbolae with:

Foci (± 3, 0) and vertices (± 2, 0)

Foci (0, ± 5) and vertices (0, ± 3)

Find their centres and equations.

Calculate eccentricity and length of latus recti, transverse and conjugate axes.

As an assignment,

Find all these values.

Slide Number 10

Assignment

Find the coordinates of the foci, vertices and eccentricity for these hyperbolae.

Also calculate length of the latus rectum and transverse and conjugate axes.

x2/16 - y2/9 = 1

49y2 – 16x2 = 784

Find all these values for these hyperbolae.
Slide Number 11

About Spoken Tutorial project

The video at the following link summarizes the Spoken Tutorial project.

Please download and watch it.

Slide Number 12

Spoken Tutorial workshops

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For more details, please write to us.

Slide Number 13

Forum for specific questions:

Do you have questions in THIS Spoken Tutorial?

Please visit this site.

Choose the minute and second where you have the question.

Explain your question briefly.

Someone from our team will answer them.

Please post your timed queries on this forum.
Slide Number 14

Acknowledgement

Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.

This is Vidhya Iyer from IIT Bombay, signing off.

Thank you for joining.

Contributors and Content Editors

Madhurig, Snehalathak, Vidhya

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