Snehalathak at 10:58, 31 August 2018

2018-08-31T10:58:25Z

Snehalathak at 10:36, 31 August 2018

2018-08-31T10:36:01Z

Madhurig at 07:04, 31 August 2018

2018-08-31T07:04:26Z

Vidhya: Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''Conic Sections - Hyperbola''' |- | | ''..."

2018-08-16T10:00:21Z

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
| | '''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 '''F1'''and '''F2''' called foci.

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.

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 and 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''' and 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'''.
|-
| | This will be one of our foci, '''F1'''.
| | This will be one of our foci, '''F1'''.
|-
| |
| | 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''' 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.
|-
| | 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 twice 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''' 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'''.
| | Circle '''d''' with center '''F2''' and radius '''a minus k''' appears.
|-
| | 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''' 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'''.
| | 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 '''c'''and '''d'''and circles '''c'''and '''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''' and 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
|-
| | 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 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''' 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'''.

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.
|-
| | 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 and 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.
|-
| | Show '''Slide Number 6'''.
| | Press '''Enter''' after each line to go to the next line.

Click '''OK'''.
|-
| | '''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
| | '''Text box for hyperbola c'''

transverse axis '''2a''' equals 4

'''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.
|-
| | 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.
|-
| | 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,'''

Construct hyperbolae with the following foci and vertices.

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'''
| | The '''Spoken Tutorial Project '''team conducts workshops and gives certificates.

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.
|-
|}

@@ Line 255: / Line 255: @@
 |-
 ||Set '''slider k''' at 2 and drag '''slider a''' to both ends.
-||First '''k''' at 2.
+||Set first '''k''' at 2.
 |-
 ||Set '''slider k''' at 3 and drag '''slider a''' to both ends.
@@ Line 327: / Line 327: @@
 |-
 ||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 drag the '''sliders''' from end to end.
 |-
 ||Point to hyperbola '''c'''.

@@ Line 40: / Line 40: @@
 For relevant tutorials, please visit our website.
 |-
-||'''Slide Number 5'''
+||'''Slide Number 5 & 6'''
 '''Hyperbola'''
@@ Line 442: / Line 442: @@
 In the '''Edit''' field, type the following text.
 |-
-||'''Slide Number 6'''.
+||'''Slide Number 7'''.
 '''Text box for Hyperbola c'''

Applications-of-GeoGebra/C2/Conic-Sections-Hyperbola/English - Revision history

Snehalathak at 10:58, 31 August 2018

Snehalathak at 10:36, 31 August 2018

Madhurig at 07:04, 31 August 2018

Vidhya: Created page with " {|border=1 | | '''Visual Cue''' | | '''Narration''' |- | | '''Slide Number 1''' '''Title Slide''' | | Welcome to this tutorial on '''Conic Sections - Hyperbola''' |- | | ''..."