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

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{|border=1
 
{|border=1
 
||'''Visual Cue'''
 
||'''Visual Cue'''
Line 5: Line 4:
  
 
|-
 
|-
−
| | '''Slide Number 1'''
+
||'''Slide Number 1'''
  
 
'''Title Slide'''
 
'''Title Slide'''
−
| | Welcome to this '''tutorial''' on '''Conic Sections – Parabola'''.
+
||Welcome to this '''tutorial''' on '''Conic Sections – Parabola'''.
 
|-
 
|-
−
| | '''Slide Number 2'''
+
||'''Slide Number 2'''
  
 
'''Learning Objectives'''
 
'''Learning Objectives'''
−
| | In this '''tutorial''', we will learn how to use '''GeoGebra''' to:
+
||In this '''tutorial''', we will learn how to use '''GeoGebra''' to:
−
Study standard equations and parts of a parabola
+
* Study standard equations and parts of a parabola
  
−
Construct parabolas
+
* Construct parabolas.
 
|-
 
|-
−
| | '''Slide Number 3'''
+
||'''Slide Number 3'''
 
'''Pre-requisites'''
 
'''Pre-requisites'''
−
| | To follow this '''tutorial''', you should have basic knowledge of
+
||To follow this '''tutorial''', you should have basic knowledge of
 
'''GeoGebra''' interface
 
'''GeoGebra''' interface
  
 
'''Conic sections''' in geometry
 
'''Conic sections''' in geometry
 
|-
 
|-
−
| s | '''Slide Number 4'''
+
|| '''Slide Number 4'''
  
 
'''System Requirement'''
 
'''System Requirement'''
−
| | Here I am using:
+
||Here I am using:
−
'''Ubuntu Linux '''OS version 14.04
+
'''Ubuntu Linux''' Operating System version 14.04
  
 
'''GeoGebra 5.0.388.0-d'''
 
'''GeoGebra 5.0.388.0-d'''
 
|-
 
|-
−
| | '''Slide Number 5'''
+
||'''Slide Number 5'''
  
 
'''Parabola'''
 
'''Parabola'''
−
 
−
[[Image:]]
 
  
 
A parabola is the '''locus''' of points equidistant from the fixed point called the focus.
 
A parabola is the '''locus''' of points equidistant from the fixed point called the focus.
  
 
The points on the parabola are also equidistant from the fixed line called the '''directrix'''.  
 
The points on the parabola are also equidistant from the fixed line called the '''directrix'''.  
−
| | A parabola is the '''locus''' of points equidistant from the fixed point called the focus.
+
||A parabola is the '''locus''' of points equidistant from the fixed point called the focus.
  
 
The points on the parabola are also equidistant from the fixed line called the '''directrix'''.  
 
The points on the parabola are also equidistant from the fixed line called the '''directrix'''.  
Line 52: Line 49:
 
'''Latus Rectum''' passes through the Focus and is perpendicular to the '''Axis of Symmetry'''.  
 
'''Latus Rectum''' passes through the Focus and is perpendicular to the '''Axis of Symmetry'''.  
 
|-
 
|-
−
| | Show the '''GeoGebra''' window.
+
||Show the '''GeoGebra''' window.
−
| | Let us construct a parabola in '''GeoGebra'''.  
+
||Let us construct a parabola in '''GeoGebra'''.  
  
 
I have already opened '''GeoGebra''' interface.
 
I have already opened '''GeoGebra''' interface.
 
|-
 
|-
−
| | Click on '''Point''' tool and click in '''Graphics''' view.  
+
||Click on '''Point''' tool and click in '''Graphics''' view.  
  
 
Point to point '''A'''.  
 
Point to point '''A'''.  
−
| | Click on '''Point''' tool and click in '''Graphics''' view.  
+
||Click on '''Point''' tool and click in '''Graphics''' view.  
  
 
This creates point '''A'''.
 
This creates point '''A'''.
 
|-
 
|-
−
| | Right-click on point '''A''' and select the '''Rename''' option.  
+
||Right-click on point '''A''' >> select the '''Rename''' option.  
−
| | Right-click on point '''A''' and select the '''Rename''' option.  
+
||Right-click on point '''A''' and select the '''Rename''' option.  
 
|-
 
|-
−
| | In '''New Name''' text box, type '''Focus''' instead of '''A'''  >> click '''OK'''.
+
||In '''New Name''' text box, type '''Focus''' instead of '''A'''  >> click '''OK'''.
  
 
Point to '''Focus'''.
 
Point to '''Focus'''.
−
| | In the '''New Name''' text box, type '''Focus''' instead of '''A '''and click '''OK'''.
+
||In the '''New Name''' text box, type '''Focus''' instead of '''A '''and click '''OK'''.
 
   
 
   
 
This renames point '''A''' as '''Focus'''.
 
This renames point '''A''' as '''Focus'''.
 
|-
 
|-
−
| | Click on '''Line''' tool >> click in two places in '''Graphics''' view below '''Focus'''.  
+
||Click on '''Line''' tool >> click in two places in '''Graphics''' view below '''Focus'''.  
  
 
Point to line '''AB'''.
 
Point to line '''AB'''.
−
| | Click on '''Line''' tool and click on two places in '''Graphics''' view, below '''Focus'''.
+
||Click on '''Line''' tool and click on two places in '''Graphics''' view, below '''Focus'''.
 
   
 
   
−
This creates line ''' AB'''.  
+
This creates line '''AB'''.  
 
|-
 
|-
−
| | Right-click on line '''AB''' >> choose '''Rename''' option.  
+
||Right-click on line '''AB''' >> choose '''Rename''' option.  
−
| | Right-click on line '''AB''' and choose the '''Rename''' option.  
+
||Right-click on line '''AB''' and choose the '''Rename''' option.  
 
|-
 
|-
−
| | Type '''directrix''' in '''New Name''' field >> click '''OK'''.  
+
||Type '''directrix''' in '''New Name''' field >> click '''OK'''.  
  
 
Point to '''directrix'''.  
 
Point to '''directrix'''.  
−
| | In the '''New Name''' field, type '''directrix''' and click '''OK'''.
+
||In the '''New Name''' field, type '''directrix''' and click '''OK'''.
  
 
This renames line '''AB''' as the '''directrix'''.  
 
This renames line '''AB''' as the '''directrix'''.  
 
|-
 
|-
−
| | Click on '''Perpendicular Line''' tool >> click on line '''AB'''.
+
||Click on '''Perpendicular Line''' tool >> click on line '''AB'''.
−
| | Click on '''Perpendicular Line''' tool, then click on line '''AB'''.
+
||Click on '''Perpendicular Line''' tool, then click on line '''AB'''.
 
|-
 
|-
−
| | Drag the '''cursor''' until '''Focus''' >> click on point '''A'''.
+
||Drag the '''cursor''' until '''Focus''' >> click on point '''A'''.
−
| | Drag the '''cursor''' until the resulting line passes through '''Focus''' and click on '''Focus'''.
+
||Drag the '''cursor''' until the resulting line passes through '''Focus''' and click on '''Focus'''.
 
|-
 
|-
−
| | Point to the perpendicular line through '''Focus'''.  
+
||Point to the perpendicular line through '''Focus'''.  
  
 
Point to '''axis of symmetry'''.
 
Point to '''axis of symmetry'''.
−
| | This draws a line perpendicular to line '''AB''', passing through '''Focus'''.
+
||This draws a line perpendicular to line '''AB''', passing through '''Focus'''.
  
  
 
This line is the '''axis of symmetry'''.
 
This line is the '''axis of symmetry'''.
 
|-
 
|-
−
| | Right-click on this line perpendicular to line '''AB'''.
+
||Right-click on this line perpendicular to line '''AB'''.
  
 
Choose the '''Rename''' option.  
 
Choose the '''Rename''' option.  
  
 
Type '''axis of symmetry''' in '''New Name''' field >> click '''OK'''.  
 
Type '''axis of symmetry''' in '''New Name''' field >> click '''OK'''.  
−
| | Right-click on this line perpendicular to line '''AB'''.
+
||Right-click on this line perpendicular to line '''AB'''.
  
 
Choose the '''Rename''' option.  
 
Choose the '''Rename''' option.  
Line 118: Line 115:
 
Click '''OK'''
 
Click '''OK'''
 
|-
 
|-
−
| | Click on '''Parabola''' tool under '''Ellipse''' tool.
+
||Click on '''Parabola''' tool under '''Ellipse''' tool.
  
 
Click on '''Focus''' and line '''AB''' ('''directrix''').
 
Click on '''Focus''' and line '''AB''' ('''directrix''').
−
| | Under '''Ellipse''' tool, click on '''Parabola''' tool.
+
||Under '''Ellipse''' tool, click on '''Parabola''' tool.
  
 
Then click on '''Focus''' and the '''directrix'''.  
 
Then click on '''Focus''' and the '''directrix'''.  
 
|-
 
|-
−
| | Point to the parabola.
+
||Point to the parabola.
−
| | This creates a parabola with its focus at '''Focus''' and with line '''AB''' as the '''directrix'''.
+
||This creates a parabola with its focus at '''Focus''' and with line '''AB''' as the '''directrix'''.
 
|-
 
|-
−
| | Click on '''Intersect''' tool. >> Click on the '''parabola''' and '''axis of symmetry'''.
+
||Click on '''Intersect''' tool. >> Click on the '''parabola''' and '''axis of symmetry'''.
−
| | Under '''Point''' tool, click on '''Intersect''' tool.  
+
||Under '''Point''' tool, click on '''Intersect''' tool.  
  
 
Click on the parabola and '''axis of symmetry'''.
 
Click on the parabola and '''axis of symmetry'''.
 
|-
 
|-
−
| | Point to point '''C'''.
+
||Point to point '''C'''.
−
| | This creates point '''C''' at the intersection.
+
||This creates point '''C''' at the intersection.
  
 
It is the '''vertex''' of the parabola.  
 
It is the '''vertex''' of the parabola.  
 
|-
 
|-
−
| | Right-click on point '''C''' >> choose the '''Rename''' option.  
+
||Right-click on point '''C''' >> choose the '''Rename''' option.  
−
| | Right-click on point '''C''' and choose the '''Rename ''' option.  
+
||Right-click on point '''C''' and choose the '''Rename ''' option.  
 
|-
 
|-
−
| | Type '''Vertex''' in '''the '''New Name''' field >> click '''OK'''.
+
||Type '''Vertex''' in '''the '''New Name''' field >> click '''OK'''.
−
| | In the '''New Name''' field, type '''Vertex''' and click '''OK'''.
+
||In the '''New Name''' field, type '''Vertex''' and click '''OK'''.
 
|-
 
|-
−
| | Click on '''Perpendicular Line''' tool >> click on the '''axis of symmetry'''.
+
||Click on '''Perpendicular Line''' tool >> click on the '''axis of symmetry'''.
−
| | Click on '''Perpendicular Line''' tool and click on the '''axis of symmetry'''.
+
||Click on '''Perpendicular Line''' tool and click on the '''axis of symmetry'''.
 
|-
 
|-
−
| | Drag the '''cursor''' until the line passes through point '''A''' (Focus) >> click on point '''A'''.
+
||Drag the '''cursor''' until the line passes through point '''A''' (Focus) >> click on point '''A'''.
−
| | Drag the '''cursor''' until the line passes through the '''Focus''' and click on it.
+
||Drag the '''cursor''' until the line passes through the '''Focus''' and click on it.
 
|-
 
|-
−
| | Point to the parallel line.
+
||Point to the parallel line.
−
| | This results in a line parallel to the '''directrix''', passing through the '''Focus'''.
+
||This results in a line parallel to the '''directrix''', passing through the '''Focus'''.
 
|-
 
|-
−
| | Click on '''Intersect''' tool under '''Point''' tool.
+
||Click on '''Intersect''' tool under '''Point''' tool.
  
  
 
Click on the intersections of the parabola and the newly drawn line through '''Focus'''.
 
Click on the intersections of the parabola and the newly drawn line through '''Focus'''.
  
−
| | Under '''Point''' tool, click on '''Intersect''' tool.
+
||Under '''Point''' tool, click on '''Intersect''' tool.
  
 
Click on the parabola and the newly drawn line through '''Focus'''.
 
Click on the parabola and the newly drawn line through '''Focus'''.
 
|-
 
|-
−
| | Point to points '''C''' and '''D'''.  
+
||Point to points '''C''' and '''D'''.  
−
| | This creates points '''C''' and '''D'''.
+
||This creates points '''C''' and '''D'''.
 
|-
 
|-
−
| | Click on '''Segment''' tool under the '''Line''' tool >> click on points '''C'''and '''D'''.
+
||Click on '''Segment''' tool under the '''Line''' tool >> click on points '''C'''and '''D'''.
−
| | Under '''Line''' tool, click on '''Segment''' tool and click on points '''C''' and '''D'''.
+
||Under '''Line''' tool, click on '''Segment''' tool and click on points '''C''' and '''D'''.
 
|-
 
|-
−
| | Point to Segment '''CD'''.  
+
||Point to Segment '''CD'''.  
−
| | Resulting Segment '''CD''' is the '''latus rectum'''.
+
||Resulting Segment '''CD''' is the '''latus rectum'''.
 
|-
 
|-
−
| | Right-click on Segment '''CD''' and choose the '''Rename''' option.
+
||Right-click on Segment '''CD''' >> choose the '''Rename''' option.
−
| | Right-click on Segment '''CD'''and choose the '''Rename''' option.
+
||Right-click on Segment '''CD''' and choose the '''Rename''' option.
 
|-
 
|-
−
| | Type '''Latus Rectum''' in the '''New Name''' field >> click '''OK''' button.
+
||Type '''Latus Rectum''' in the '''New Name''' field >> click '''OK''' button.
−
| | In the '''New Name''' field, type '''Latus Rectum''' and click '''OK'''.
+
||In the '''New Name''' field, type '''Latus Rectum''' and click '''OK'''.
 
|-
 
|-
−
| | Move the '''Latus''' label so you can see it properly.  
+
||Move the '''Latus''' label so you can see it properly.  
−
| | Move the '''Latus''' label so you can see it properly.  
+
||Move the '''Latus''' label so you can see it properly.  
 
|-
 
|-
−
| | Click and drag '''Graphics''' view to see the parabola properly.  
+
||Click >> drag '''Graphics''' view to see the parabola properly.  
−
| | Click and drag '''Graphics''' view to see the parabola properly.  
+
||Click and drag '''Graphics''' view to see the parabola properly.  
 
|-
 
|-
−
| | Point to '''Algebra''' view.
+
||Point to '''Algebra''' view.
  
 
Drag boundary so you can see equation properly.  
 
Drag boundary so you can see equation properly.  
  
−
| | In '''Algebra''' view, you can see the equation describing the parabola.
+
||In '''Algebra''' view, you can see the equation describing the parabola.
  
 
Drag boundary so you can see the equation properly.  
 
Drag boundary so you can see the equation properly.  
Line 193: Line 190:
 
Also, you can see the equations for the '''axis of symmetry, directrix''' and '''latus rectum'''.
 
Also, you can see the equations for the '''axis of symmetry, directrix''' and '''latus rectum'''.
 
|-
 
|-
−
| | Drag boundary so you can see '''Graphics''' view properly again.  
+
||Drag boundary so you can see '''Graphics''' view properly.  
−
| | Drag boundary so you can see '''Graphics''' view properly again.  
+
||Drag boundary so you can see '''Graphics''' view properly again.  
 
|-
 
|-
−
| | Click in '''Graphics''' view and drag background.  
+
||Click in '''Graphics''' view and drag background.  
−
| | Click in '''Graphics''' view and drag background.  
+
||Click in '''Graphics''' view and drag background.  
 
|-
 
|-
−
| | Click on '''Intersect''' tool under '''Point''' tool.
+
||Click on '''Intersect''' tool under '''Point''' tool.
  
 
Click on the intersection of the '''axis of symmetry''' and the '''directrix'''.
 
Click on the intersection of the '''axis of symmetry''' and the '''directrix'''.
−
| | Under '''Point''' tool, click on '''Intersect''' tool.
+
||Under '''Point''' tool, click on '''Intersect''' tool.
  
 
Click on '''axis of symmetry''' and '''directrix'''.
 
Click on '''axis of symmetry''' and '''directrix'''.
 
|-
 
|-
−
| | Point to point '''E'''.
+
||Point to point '''E'''.
−
| | This creates point '''E'''.
+
||This creates point '''E'''.
 
|-
 
|-
−
| | Click on '''Distance or Length''' tool under '''Angle''' tool.  
+
||Click on '''Distance or Length''' tool under '''Angle''' tool.  
−
| | Under '''Angle''' tool, click on '''Distance or Length''' tool.  
+
||Under '''Angle''' tool, click on '''Distance or Length''' tool.  
 
|-
 
|-
−
| | Click on '''Focus''' >> '''Vertex'''.
+
||Click on '''Focus''' >> '''Vertex'''.
−
| | Click on '''Focus''' and '''Vertex'''.  
+
||Click on '''Focus''' and '''Vertex'''.  
 
|-
 
|-
−
| | Point to the distance of '''FocusVertex''' appearing in '''Graphics''' view.
+
||Point to the distance of '''FocusVertex''' appearing in '''Graphics''' view.
−
 
+
||Note the distance of '''FocusVertex''' appearing in '''Graphics''' view.
−
| | Note the distance of '''FocusVertex''' appearing in '''Graphics''' view.
+
 
|-
 
|-
−
| | Click on '''Vertex''' >> point '''E'''.
+
||Click on '''Vertex''' >> point '''E'''.
−
| | Click on '''Vertex''' and point '''E'''.
+
||Click on '''Vertex''' and point '''E'''.
 
|-  
 
|-  
−
| | Point to the distance of '''Vertex E''' appearing in '''Graphics''' view.
+
||Point to the distance of '''Vertex E''' appearing in '''Graphics''' view.
−
| | Note the distance of '''Vertex E''' appearing in '''Graphics''' view.
+
||Note the distance of '''Vertex E''' appearing in '''Graphics''' view.
  
 
Both these distances are equal.  
 
Both these distances are equal.  
 
|-
 
|-
−
| |  
+
||
−
| | Let us look at the general equations of parabolas.
+
||Let us look at the general equations of parabolas.
 
|-
 
|-
−
| | Show the new '''GeoGebra''' window.
+
||Show the new '''GeoGebra''' window.
−
| | I have opened a new '''GeoGebra''' window.
+
||I have opened a new '''GeoGebra''' window.
 
|-
 
|-
−
| | Type '''(x-a)^2=4 p (y-b)''' in '''input bar''' >> press '''Enter'''.
+
||Type '''(x-a)^2=4 p (y-b)''' in '''input bar''' >> press '''Enter'''.
−
| | In '''input bar''', type '''x minus a in parentheses caret 2 equals 4 space p space y minus b in parentheses'''.  
+
||In '''input bar''', type '''x minus a in parentheses caret 2 equals 4 space p space y minus b''' in parentheses'''.  
  
 
To type '''caret symbol''', hold '''Shift''' key down and press 6.  
 
To type '''caret symbol''', hold '''Shift''' key down and press 6.  
Line 242: Line 238:
 
Press '''Enter'''.  
 
Press '''Enter'''.  
 
|-
 
|-
−
| | Point to '''Create Sliders''' window
+
||Point to '''Create Sliders''' window
−
| | '''Create Sliders''' window pops up asking if you want to create '''sliders''' for '''a, b''' and '''p'''.
+
||'''Create Sliders''' window pops up asking if you want to create '''sliders''' for '''a, b''' and '''p'''.
 
|-
 
|-
−
| | Click on '''Create Sliders'''.  
+
||Click on '''Create Sliders'''.  
−
| | Click on '''Create Sliders'''.
+
||Click on '''Create Sliders'''.
 
|-
 
|-
−
| | Point to '''sliders a, p''' and '''b'''.  
+
||Point to '''sliders a, p''' and '''b'''.  
−
| | '''Sliders''' are created for '''a, p''' and '''b'''.
+
||'''Sliders''' are created for '''a, p''' and '''b'''.
  
 
The '''default''' setting for all three '''coefficients''' is 1.
 
The '''default''' setting for all three '''coefficients''' is 1.
 
|-
 
|-
−
| | A parabola opening upwards appears in '''Graphics''' view.
+
||A parabola opening upwards appears in '''Graphics''' view.
  
 
Point to '''vertex''' of parabola.  
 
Point to '''vertex''' of parabola.  
−
| | A parabola opening upwards appears in '''Graphics''' view.
+
||A parabola opening upwards appears in '''Graphics''' view.
  
 
'''a comma b''' correspond to the '''co-ordinates''' of the '''vertex'''.
 
'''a comma b''' correspond to the '''co-ordinates''' of the '''vertex'''.
 
|-
 
|-
−
| | Double click on parabola >> click on '''Object Properties''' and then on '''Color''' tab.
+
||Double click on parabola >> click on '''Object Properties''' and then on '''Color''' tab.
−
| | Double click on the parabola, click on '''Object Properties''' and then on '''Color''' tab.
+
||Double click on the parabola, click on '''Object Properties''' and then on '''Color''' tab.
 
|-
 
|-
−
| | Select red and close the '''Preferences''' box.
+
||Select red >> close the '''Preferences''' box.
−
| | Select red and close the '''Preferences''' box.
+
||Select red and close the '''Preferences''' box.
 
|-
 
|-
−
| | Point to the red parabola and its equation  in '''Graphics''' and '''Algebra''' views.
+
||Point to the red parabola and its equation  in '''Graphics''' and '''Algebra''' views.
−
| | The parabola and its equation appear red in the '''Graphics''' and '''Algebra''' views.
+
||The parabola and its equation appear red in the '''Graphics''' and '''Algebra''' views.
 
|-
 
|-
−
| | Move boundary so you can see the equation properly.  
+
||Move boundary so you can see the equation properly.  
−
| | Move boundary so you can see the equation properly.  
+
||Move boundary so you can see the equation properly.  
 
|-
 
|-
−
| | Right-click on '''slider a''' button >> check '''Animation On''' option.
+
||Right-click on '''slider a''' button >> check '''Animation On''' option.
−
| | Right-click on '''slider a''' and check '''Animation On''' option.
+
||Right-click on '''slider a''' and check '''Animation On''' option.
 
|-
 
|-
−
| | Point to the parabola in '''Graphics''' view.  
+
||Point to the parabola in '''Graphics''' view.  
−
| | Note the effects on the horizontal movement of the red parabola.  
+
||Note the effects on the horizontal movement of the red parabola.  
 
|-
 
|-
−
| | Right-click on '''slider a''' >> uncheck '''Animation On''' option.
+
||Right-click on '''slider a''' >> uncheck '''Animation On''' option.
−
| | Right-click on '''slider a''' and uncheck '''Animation On''' option.
+
||Right-click on '''slider a''' and uncheck '''Animation On''' option.
 
|-
 
|-
−
| | Right-click on '''slider p''' >> check '''Animation On''' option.
+
||Right-click on '''slider p''' >> check '''Animation On''' option.
−
| | Right-click on '''slider p''' and check '''Animation On''' option.
+
||Right-click on '''slider p''' and check '''Animation On''' option.
 
|-
 
|-
−
| | Point to parabola in '''Graphics view'''.
+
||Point to parabola in '''Graphics view'''.
−
| | Note the effects on the shape and orientation of the parabola.  
+
||Note the effects on the shape and orientation of the parabola.  
 
|-
 
|-
−
| | Right-click on '''slider p''' >> uncheck '''Animation On''' option.
+
||Right-click on '''slider p''' >> uncheck '''Animation On''' option.
−
| | Right-click on '''slider p''' and uncheck '''Animation On''' option.
+
||Right-click on '''slider p''' and uncheck '''Animation On''' option.
 
|-
 
|-
−
| | Right-click on '''slider b''' >> check '''Animation On''' option.
+
||Right-click on '''slider b''' >> check '''Animation On''' option.
−
| | Right-click on '''slider b''' and check '''Animation On''' option.
+
||Right-click on '''slider b''' and check '''Animation On''' option.
 
|-  
 
|-  
−
| | Point to the parabola.  
+
||Point to the parabola.  
−
| | Note the effects on the vertical movement of the parabola.  
+
||Note the effects on the vertical movement of the parabola.  
 
|-
 
|-
−
| | Right-click on '''slider b''' >> uncheck '''Animation On''' option.
+
||Right-click on '''slider b''' >> uncheck '''Animation On''' option.
−
| | Right-click on '''slider b''' and uncheck '''Animation On''' option.
+
||Right-click on '''slider b''' and uncheck '''Animation On''' option.
 
|-
 
|-
−
| | Point to '''sliders a, p''' and '''b''' (all = 1) and the red parabola '''c''' in '''Graphics '''view.
+
||Point to '''sliders a, p''' and '''b''' (all = 1) and the red parabola '''c''' in '''Graphics '''view.
  
 
Click on parabola '''c''' in '''Graphics''' view and note highlighting of equation '''c''' in '''Algebra''' view.  
 
Click on parabola '''c''' in '''Graphics''' view and note highlighting of equation '''c''' in '''Algebra''' view.  
  
 
Point to equation '''c: (x<sup>2</sup>-2x-4y) = -5''' in '''Algebra''' view.
 
Point to equation '''c: (x<sup>2</sup>-2x-4y) = -5''' in '''Algebra''' view.
−
| | Note that when '''a''', '''p''' and '''b '''are equal to 1, the red parabola '''c''' is described by equation '''c'''.  
+
||Note that when '''a''', '''p''' and '''b '''are equal to 1, the red parabola '''c''' is described by equation '''c'''.  
  
 
Click on parabola '''c''' in '''Graphics''' view and note highlighting of equation '''c''' in '''Algebra''' view.  
 
Click on parabola '''c''' in '''Graphics''' view and note highlighting of equation '''c''' in '''Algebra''' view.  
  
−
Equation '''c''' is given by '''x squared minus 2x minus 4y equals minus 5'''.
+
Equation '''c''' is given by x squared minus 2x minus 4y equals minus 5.
 
|-
 
|-
−
| | Type '''Focus(c)''' in '''input bar'''>> press '''Enter'''.  
+
||Type '''Focus(c)''' in '''input bar'''>> press '''Enter'''.  
  
 
Point to point '''A''' in '''Graphics''' view.  
 
Point to point '''A''' in '''Graphics''' view.  
−
| | In '''input bar''', type '''Focus c in parentheses'''.
+
||In '''input bar''', type '''Focus c''' in parentheses.
  
 
Press '''Enter'''.  
 
Press '''Enter'''.  
Line 319: Line 315:
 
'''Focus''' is drawn at point '''A ''' in '''Graphics''' view.  
 
'''Focus''' is drawn at point '''A ''' in '''Graphics''' view.  
 
|-
 
|-
−
| | Point to the '''coordinates''' of point '''A''', the '''Focus''', in '''Algebra''' view.  
+
||Point to the '''coordinates''' of point '''A''', the '''Focus''', in '''Algebra''' view.  
−
| | The coordinates of '''Focus''' of parabola '''c''', which is point '''A''', appear in '''Algebra''' view.  
+
||The coordinates of '''Focus''' of parabola '''c''', which is point '''A''', appear in '''Algebra''' view.  
 
|-
 
|-
−
| | Type '''Vertex(c)''' in '''input bar'''>> press '''Enter'''.  
+
||Type '''Vertex(c)''' in '''input bar'''>> press '''Enter'''.  
  
 
Point to point '''B''' in '''Graphics''' view.  
 
Point to point '''B''' in '''Graphics''' view.  
−
| | In '''input bar''', type '''Vertex c in parentheses'''.  
+
||In '''input bar''', type '''Vertex c''' in parentheses.  
  
 
Press '''Enter'''.  
 
Press '''Enter'''.  
Line 331: Line 327:
 
'''Vertex''' is drawn at point '''B''' in '''Graphics''' view.  
 
'''Vertex''' is drawn at point '''B''' in '''Graphics''' view.  
 
|-
 
|-
−
| | Point to the '''coordinates''' of point '''B''' in '''Algebra''' view.  
+
||Point to the '''coordinates''' of point '''B''' in '''Algebra''' view.  
−
| | The '''coordinates''' of '''Vertex''' of parabola '''c''', which is point '''B''', appear in '''Algebra''' view.  
+
||The '''coordinates''' of '''Vertex''' of parabola '''c''', which is point '''B''', appear in '''Algebra''' view.  
 
|-
 
|-
−
| | Type '''Directrix(c)''' in '''input bar''' >> press '''Enter'''.
+
||Type '''Directrix(c)''' in '''input bar''' >> press '''Enter'''.
  
  
 
Point to '''Directrix''' in '''Graphics''' view.  
 
Point to '''Directrix''' in '''Graphics''' view.  
−
| | In '''input bar''', type '''Directrix c''' in parentheses.
+
||In '''input bar''', type '''Directrix c''' in parentheses.
  
 
Press '''Enter'''.
 
Press '''Enter'''.
Line 344: Line 340:
 
'''Directrix''' appears as a line along '''x axis''' in '''Graphics''' view.  
 
'''Directrix''' appears as a line along '''x axis''' in '''Graphics''' view.  
 
|-
 
|-
−
| | Point to the equation, '''y=0''', in '''Algebra''' view.  
+
||Point to the equation, '''y=0''', in '''Algebra''' view.  
−
| | The equation for the '''Directrix''' of parabola '''c''', '''y equals 0''', appears in '''Algebra''' view.  
+
||The equation for the '''Directrix''' of parabola '''c''', '''y equals 0''', appears in '''Algebra''' view.  
 
|-
 
|-
−
| | Double click on '''Directrix''' in '''Graphics''' view >> '''Redefine''' text box >> '''Object Properties''' >> '''Color''' tab.
+
||Double click on '''Directrix''' in '''Graphics''' view >> '''Redefine''' text box >> '''Object Properties''' >> '''Color''' tab.
−
| | Double click on '''Directrix''' in '''Graphics''' view.   
+
||Double click on '''Directrix''' in '''Graphics''' view.   
  
−
In the '''Redefine''' text box, click on '''Object Properties''', then on the '''Color''' tab.  
+
In the '''Redefine''' text box, click on '''Object Properties''', then the '''Color''' tab.  
 
|-
 
|-
−
| | In the left panel, point to highlighted '''Directrix''', identify '''Focus''' and ''' Vertex''' created for parabola '''c'''.
+
||In the left panel, point to highlighted '''Directrix''', identify '''Focus''' and ''' Vertex''' created for parabola '''c'''.
−
| | In the left panel, note that the '''Directrix''' is highlighted.  
+
||In the left panel, note that the '''Directrix''' is highlighted.  
  
 
Identify '''Focus''' and '''Vertex''' created for parabola '''c'''.
 
Identify '''Focus''' and '''Vertex''' created for parabola '''c'''.
 
|-
 
|-
−
| | Click on each one to highlight while pressing the '''Control''' key.  
+
||Click on each one to highlight while pressing the '''Control''' key.  
−
| | While pressing the '''Control''' key, click and highlight '''Focus''' and '''Vertex'''.  
+
||While pressing the '''Control''' key, click and highlight '''Focus''' and '''Vertex'''.  
 
|-
 
|-
−
| | Click on red.  
+
||Click on red.  
−
| | Click on red.  
+
||Click on red.  
 
|-
 
|-
−
| | Close the '''Preferences''' box.  
+
||Close the '''Preferences''' box.  
−
| | Close the '''Preferences''' box.  
+
||Close the '''Preferences''' box.  
 
|-
 
|-
−
| | Point to '''Focus''', '''Vertex''' and '''Directrix''' and their '''co-ordinates''' and equation in '''Graphics''' and '''Algebra''' views.  
+
||Point to '''Focus''', '''Vertex''' and '''Directrix''' and their '''co-ordinates''' and equation in '''Graphics''' and '''Algebra''' views.  
−
| | For parabola '''c''', '''Focus''', '''Vertex''' and '''Directrix''' and their '''coordinates''' and equation appear red.  
+
||For parabola '''c''', '''Focus''', '''Vertex''' and '''Directrix''' and their '''coordinates''' and equation appear red.  
 
|-
 
|-
−
| |Show '''Geogebra''' window with parabolas '''c''' and '''d'''.   
+
||Show '''Geogebra''' window with parabolas '''c''' and '''d'''.   
  
 
In '''Algebra''' view, point to equation '''d''' and in '''Graphics''' view, point to parabola '''d'''.   
 
In '''Algebra''' view, point to equation '''d''' and in '''Graphics''' view, point to parabola '''d'''.   
−
| |Follow the earlier steps to construct parabola '''d'''.
+
||Follow the earlier steps to construct parabola '''d'''.
 
|-
 
|-
−
| |  
+
||
−
| | Let us summarize.
+
||Let us summarize.
 
|-
 
|-
−
| | '''Slide Number 6'''
+
||'''Slide Number 6'''
  
 
'''Summary'''
 
'''Summary'''
−
| | In this '''tutorial''', we have learnt how to use '''GeoGebra''' to:
+
||In this '''tutorial''', we have learnt how to use '''GeoGebra''' to:
−
Study the standard equations and parts of a parabola
+
* Study the standard equations and parts of a parabola
  
−
Construct parabolas
+
* Construct parabolas
 
|-
 
|-
−
| | '''Slide Number 7'''
+
||'''Slide Number 7'''
 
'''Assignment'''
 
'''Assignment'''
  
Line 395: Line 391:
  
 
Find their equations.  
 
Find their equations.  
−
| | As an assignment:
+
||As an assignment:
 
Try these steps to construct parabolas with these '''foci''' and '''directrices'''.  
 
Try these steps to construct parabolas with these '''foci''' and '''directrices'''.  
  
 
Find their equations.  
 
Find their equations.  
 
|-
 
|-
−
| | '''Slide Number 8'''
+
||'''Slide Number 8'''
 
'''Assignment'''
 
'''Assignment'''
  
Line 410: Line 406:
  
 
x<sup>2</sup> = -16y
 
x<sup>2</sup> = -16y
−
| | As an assignment:
+
||As an assignment:
 
Find the coordinates of the '''foci''' and length of the '''latus recti''' for these parabolas.  
 
Find the coordinates of the '''foci''' and length of the '''latus recti''' for these parabolas.  
  
 
Also, find the equations of the '''axes of symmetry''' and '''directrices'''.  
 
Also, find the equations of the '''axes of symmetry''' and '''directrices'''.  
 
|-
 
|-
−
| | '''Slide Number 9'''
+
||'''Slide Number 9'''
 
'''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 10'''
+
||'''Slide Number 10'''
 
'''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 11'''
+
||'''Slide Number 11'''
 
'''Forum for specific questions:'''
 
'''Forum for specific questions:'''
  
Line 439: Line 435:
  
 
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 12'''
+
||'''Slide Number 12'''
 
'''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 16:51, 17 July 2018

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this tutorial on Conic Sections – Parabola.
Slide Number 2

Learning Objectives

In this tutorial, we will learn how to use GeoGebra to:
  • Study standard equations and parts of a parabola
  • Construct parabolas.
Slide Number 3

Pre-requisites

To follow this tutorial, you should have basic knowledge of

GeoGebra interface

Conic sections in geometry

Slide Number 4

System Requirement

Here I am using:

Ubuntu Linux Operating System version 14.04

GeoGebra 5.0.388.0-d

Slide Number 5

Parabola

A parabola is the locus of points equidistant from the fixed point called the focus.

The points on the parabola are also equidistant from the fixed line called the directrix.

A parabola is the locus of points equidistant from the fixed point called the focus.

The points on the parabola are also equidistant from the fixed line called the directrix.

Observe the different features of the parabola in the image.

The Axis of Symmetry is perpendicular to the Directrix and passes through the Focus and Vertex.

Latus Rectum passes through the Focus and is perpendicular to the Axis of Symmetry.

Show the GeoGebra window. Let us construct a parabola in GeoGebra.

I have already opened GeoGebra interface.

Click on Point tool and click in Graphics view.

Point to point A.

Click on Point tool and click in Graphics view.

This creates point A.

Right-click on point A >> select the Rename option. Right-click on point A and select the Rename option.
In New Name text box, type Focus instead of A >> click OK.

Point to Focus.

In the New Name text box, type Focus instead of A and click OK.

This renames point A as Focus.

Click on Line tool >> click in two places in Graphics view below Focus.

Point to line AB.

Click on Line tool and click on two places in Graphics view, below Focus.

This creates line AB.

Right-click on line AB >> choose Rename option. Right-click on line AB and choose the Rename option.
Type directrix in New Name field >> click OK.

Point to directrix.

In the New Name field, type directrix and click OK.

This renames line AB as the directrix.

Click on Perpendicular Line tool >> click on line AB. Click on Perpendicular Line tool, then click on line AB.
Drag the cursor until Focus >> click on point A. Drag the cursor until the resulting line passes through Focus and click on Focus.
Point to the perpendicular line through Focus.

Point to axis of symmetry.

This draws a line perpendicular to line AB, passing through Focus.


This line is the axis of symmetry.

Right-click on this line perpendicular to line AB.

Choose the Rename option.

Type axis of symmetry in New Name field >> click OK.

Right-click on this line perpendicular to line AB.

Choose the Rename option.

Type axis of symmetry in New Name field.

Click OK

Click on Parabola tool under Ellipse tool.

Click on Focus and line AB (directrix).

Under Ellipse tool, click on Parabola tool.

Then click on Focus and the directrix.

Point to the parabola. This creates a parabola with its focus at Focus and with line AB as the directrix.
Click on Intersect tool. >> Click on the parabola and axis of symmetry. Under Point tool, click on Intersect tool.

Click on the parabola and axis of symmetry.

Point to point C. This creates point C at the intersection.

It is the vertex of the parabola.

Right-click on point C >> choose the Rename option. Right-click on point C and choose the Rename option.
Type Vertex in the New Name field >> click OK. In the New Name field, type Vertex and click OK.
Click on Perpendicular Line tool >> click on the axis of symmetry. Click on Perpendicular Line tool and click on the axis of symmetry.
Drag the cursor until the line passes through point A (Focus) >> click on point A. Drag the cursor until the line passes through the Focus and click on it.
Point to the parallel line. This results in a line parallel to the directrix, passing through the Focus.
Click on Intersect tool under Point tool.


Click on the intersections of the parabola and the newly drawn line through Focus.

Under Point tool, click on Intersect tool.

Click on the parabola and the newly drawn line through Focus.

Point to points C and D. This creates points C and D.
Click on Segment tool under the Line tool >> click on points Cand D. Under Line tool, click on Segment tool and click on points C and D.
Point to Segment CD. Resulting Segment CD is the latus rectum.
Right-click on Segment CD >> choose the Rename option. Right-click on Segment CD and choose the Rename option.
Type Latus Rectum in the New Name field >> click OK button. In the New Name field, type Latus Rectum and click OK.
Move the Latus label so you can see it properly. Move the Latus label so you can see it properly.
Click >> drag Graphics view to see the parabola properly. Click and drag Graphics view to see the parabola properly.
Point to Algebra view.

Drag boundary so you can see equation properly.

In Algebra view, you can see the equation describing the parabola.

Drag boundary so you can see the equation properly.

Also, you can see the equations for the axis of symmetry, directrix and latus rectum.

Drag boundary so you can see Graphics view properly. Drag boundary so you can see Graphics view properly again.
Click in Graphics view and drag background. Click in Graphics view and drag background.
Click on Intersect tool under Point tool.

Click on the intersection of the axis of symmetry and the directrix.

Under Point tool, click on Intersect tool.

Click on axis of symmetry and directrix.

Point to point E. This creates point E.
Click on Distance or Length tool under Angle tool. Under Angle tool, click on Distance or Length tool.
Click on Focus >> Vertex. Click on Focus and Vertex.
Point to the distance of FocusVertex appearing in Graphics view. Note the distance of FocusVertex appearing in Graphics view.
Click on Vertex >> point E. Click on Vertex and point E.
Point to the distance of Vertex E appearing in Graphics view. Note the distance of Vertex E appearing in Graphics view.

Both these distances are equal.

Let us look at the general equations of parabolas.
Show the new GeoGebra window. I have opened a new GeoGebra window.
Type (x-a)^2=4 p (y-b) in input bar >> press Enter. In input bar, type x minus a in parentheses caret 2 equals 4 space p space y minus b in parentheses.

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

Note that the spaces denote multiplication.

Press Enter.

Point to Create Sliders window Create Sliders window pops up asking if you want to create sliders for a, b and p.
Click on Create Sliders. Click on Create Sliders.
Point to sliders a, p and b. Sliders are created for a, p and b.

The default setting for all three coefficients is 1.

A parabola opening upwards appears in Graphics view.

Point to vertex of parabola.

A parabola opening upwards appears in Graphics view.

a comma b correspond to the co-ordinates of the vertex.

Double click on parabola >> click on Object Properties and then on Color tab. Double click on the parabola, click on Object Properties and then on Color tab.
Select red >> close the Preferences box. Select red and close the Preferences box.
Point to the red parabola and its equation in Graphics and Algebra views. The parabola and its equation appear red in the Graphics and Algebra views.
Move boundary so you can see the equation properly. Move boundary so you can see the equation properly.
Right-click on slider a button >> check Animation On option. Right-click on slider a and check Animation On option.
Point to the parabola in Graphics view. Note the effects on the horizontal movement of the red parabola.
Right-click on slider a >> uncheck Animation On option. Right-click on slider a and uncheck Animation On option.
Right-click on slider p >> check Animation On option. Right-click on slider p and check Animation On option.
Point to parabola in Graphics view. Note the effects on the shape and orientation of the parabola.
Right-click on slider p >> uncheck Animation On option. Right-click on slider p and uncheck Animation On option.
Right-click on slider b >> check Animation On option. Right-click on slider b and check Animation On option.
Point to the parabola. Note the effects on the vertical movement of the parabola.
Right-click on slider b >> uncheck Animation On option. Right-click on slider b and uncheck Animation On option.
Point to sliders a, p and b (all = 1) and the red parabola c in Graphics view.

Click on parabola c in Graphics view and note highlighting of equation c in Algebra view.

Point to equation c: (x2-2x-4y) = -5 in Algebra view.

Note that when a, p and b are equal to 1, the red parabola c is described by equation c.

Click on parabola c in Graphics view and note highlighting of equation c in Algebra view.

Equation c is given by x squared minus 2x minus 4y equals minus 5.

Type Focus(c) in input bar>> press Enter.

Point to point A in Graphics view.

In input bar, type Focus c in parentheses.

Press Enter.

Focus is drawn at point A in Graphics view.

Point to the coordinates of point A, the Focus, in Algebra view. The coordinates of Focus of parabola c, which is point A, appear in Algebra view.
Type Vertex(c) in input bar>> press Enter.

Point to point B in Graphics view.

In input bar, type Vertex c in parentheses.

Press Enter.

Vertex is drawn at point B in Graphics view.

Point to the coordinates of point B in Algebra view. The coordinates of Vertex of parabola c, which is point B, appear in Algebra view.
Type Directrix(c) in input bar >> press Enter.


Point to Directrix in Graphics view.

In input bar, type Directrix c in parentheses.

Press Enter.

Directrix appears as a line along x axis in Graphics view.

Point to the equation, y=0, in Algebra view. The equation for the Directrix of parabola c, y equals 0, appears in Algebra view.
Double click on Directrix in Graphics view >> Redefine text box >> Object Properties >> Color tab. Double click on Directrix in Graphics view.

In the Redefine text box, click on Object Properties, then the Color tab.

In the left panel, point to highlighted Directrix, identify Focus and Vertex created for parabola c. In the left panel, note that the Directrix is highlighted.

Identify Focus and Vertex created for parabola c.

Click on each one to highlight while pressing the Control key. While pressing the Control key, click and highlight Focus and Vertex.
Click on red. Click on red.
Close the Preferences box. Close the Preferences box.
Point to Focus, Vertex and Directrix and their co-ordinates and equation in Graphics and Algebra views. For parabola c, Focus, Vertex and Directrix and their coordinates and equation appear red.
Show Geogebra window with parabolas c and d.

In Algebra view, point to equation d and in Graphics view, point to parabola d.

Follow the earlier steps to construct parabola d.
Let us summarize.
Slide Number 6

Summary

In this tutorial, we have learnt how to use GeoGebra to:
  • Study the standard equations and parts of a parabola
  • Construct parabolas
Slide Number 7

Assignment

Try these steps to construct parabolas with:

Focus (6,0) and directrix x = -6

Focus (0,-3) and directrix y = 3

Find their equations.

As an assignment:

Try these steps to construct parabolas with these foci and directrices.

Find their equations.

Slide Number 8

Assignment

Find the coordinates of the foci and length of latus recti for these parabolas.

Also, find the equations of the axes of symmetry and directrices.

y2 = 12x

x2 = -16y

As an assignment:

Find the coordinates of the foci and length of the latus recti for these parabolas.

Also, find the equations of the axes of symmetry and directrices.

Slide Number 9

About Spoken Tutorial Project

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

Please download and watch it.

Slide Number 10

Spoken Tutorial workshops

The Spoken Tutorial Project team conducts workshops and gives certificates.

For more details, please write to us.

Slide Number 11

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 12

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, Vidhya

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