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

Madhurig at 10:20, 24 July 2018

2018-07-24T10:20:57Z

Vidhya at 06:24, 19 July 2018

2018-07-19T06:24:49Z

Madhurig at 11:41, 17 July 2018

2018-07-17T11:41:56Z

Madhurig at 11:21, 17 July 2018

2018-07-17T11:21:20Z

Show changes

Vidhya at 06:48, 13 July 2018

2018-07-13T06:48:02Z

Vidhya at 06:44, 13 July 2018

2018-07-13T06:44:08Z

Vidhya at 16:16, 30 June 2018

2018-06-30T16:16:08Z

Show changes

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

2018-04-03T09:36:36Z

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

New page

{|border=1
||'''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
|-
| s | '''Slide Number 4'''

'''System Requirement'''
| | Here I am using:
'''Ubuntu Linux '''OS version 14.04

'''GeoGebra 5.0.388.0-d'''
|-
| | '''Slide Number 5'''

'''Parabola'''

[[Image:]]

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''' 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'''.

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 '''C'''and '''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''' 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.
| | 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 and 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 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 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 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.
| | 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 >> '''Object Properties''' >> '''Color''' tab.
| | Double click on '''Directrix''' in '''Graphics''' view.

Choose '''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.
|-
| | Type '''(y-l)^2=4 p (x-m)''' in the '''input bar''' >> press '''Enter'''.
| | In '''input bar''', type '''y minus l in parentheses caret 2 equals 4 space p space x minus m in parentheses'''.

Press '''Enter'''.
|-
| | Point to the pop-up window asking if you want to create '''sliders''' for '''l''' and '''m'''.
| | A window pops up asking if you want to create '''sliders''' for '''l''' and '''m'''.
|-
| | Click on '''Create Sliders'''.
| | Click on '''Create Sliders'''.
|-
| | Point to '''sliders l''' and '''m'''.
| | '''Sliders''' are created for '''l''' and '''m'''.

The '''default''' setting for both '''coefficients''' is 1.
|-
| | Point to the parabola opening to the right appears in '''Graphics''' view.

Point to the '''vertex''' of the parabola.
| | A parabola opening to the right appears in '''Graphics''' view.

'''l comma m''' correspond to the '''co-ordinates''' of the '''vertex'''.
|-
| | Double click on it, click on '''Object Properties''' >> '''Color''' tab >> select blue
| | Double click on the parabola, click on '''Object Properties'''.

Select '''Color''' tab and choose blue.
|-
| | Close the '''Preferences''' box.
| | Close the '''Preferences''' box.
|-
| | Point to parabola '''d''' and its equation '''d''' in the '''Graphics''' and '''Algebra''' views.
| | Parabola '''d''' and its equation '''d''' appear blue in '''Graphics''' and '''Algebra''' views.
|-
| | Drag '''sliders l''' and '''m''' to 2.
| | Drag '''sliders l''' and '''m''' to 2.
|-
| | Point to '''sliders l = m = 2''' and '''p = 1''', and the blue parabola '''d''' in '''Graphics''' view.

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

Point to equation '''d: y2-4x-4y= -12''' in '''Algebra''' view.
| | Note that when '''l''' and '''m''' are equal to 2, and '''p''' equals 1, the blue parabola '''d''' is described by equation '''d'''.

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

Equation '''d''' is given by '''y squared minus 4x minus 4y equals minus 12'''.
|-
| | Right-click on '''slider l''' >> check '''Animation On''' option.
| | Right-click on '''slider l''' and check '''Animation On''' option.
|-
| | Point to parabola in '''Graphics''' view.
| | Note the effects on the vertical movement of the parabola.
|-
| | Right-click on '''slider l''' >> uncheck '''Animation On''' option.
| | Right-click on '''slider l''' and uncheck '''Animation On''' option.
|-
| | Right-click on '''slider m''' >> check '''Animation On''' option.
| | Right-click on '''slider m''' and check '''Animation On'''option.
|-
| | Point to parabola in '''Graphics''' view.
| | Note the effects on the horizontal movement of the parabola.
|-
| | Right-click on '''slider m''' >> uncheck '''Animation On''' option.
| | Right-click on '''slider m''' and uncheck '''Animation On''' option.
|-
| | Type '''Focus(d)''' in the '''input bar''' >> press '''Enter'''.
| | In '''input bar''', type '''Focus d''' in parentheses.

Press '''Enter'''.
|-
| | Type '''Vertex(d)''' in the ''input bar''' >> press '''Enter'''.
| | In '''input bar''', type '''Vertex d''' in parentheses.

Press '''Enter'''.
|-
| | Type '''Directrix(d)''' in the '''input bar''' >> press '''Enter'''.
| | In '''input bar''', type '''Directrix d''' in parentheses.

Press '''Enter'''.
|-
| | Double click on '''Focus''' in '''Graphics''' view >> '''Object Properties''' >> '''Color''' tab.
| | Double click on '''Focus''' in '''Graphics''' view.

Choose '''Object Properties''', then the '''Color''' tab.
|-
| | In the left panel, point to highlighted '''Focus''' (point '''C''').

Point to '''Vertex''' and '''Directrix''' for parabola '''d'''.
| | In the left panel, note that '''Focus''', point '''C''', is highlighted.

Identify '''Vertex''' and '''Directrix''' for parabola '''d'''.
|-
| | Click on each one to highlight while pressing the '''Control''' key.
| | While pressing the '''Control''' key, click and highlight '''Vertex''' and '''Directrix'''.
|-
| | Click on Blue.
| | Click on Blue.
|-
| | Close the '''Preferences''' box.
| | Close the '''Preferences''' box.
|-
| | Right-click on '''slider a''' >> choose '''Animation On''' option to check it.
| | Right-click on '''slider a''' and choose '''Animation On''' option to check it.

Notice that this only affects the red parabola.
|-
| | Right-click on '''slider a''' and uncheck '''Animation On''' option.

Drag '''slider a''' so we can see the red parabola better.
| | Right-click and uncheck '''Animation On''' option for '''slider a'''.

Let us drag '''a''' so we can see the red parabola better.
|-
| | Drag '''b''' so you can see the vertical movement of parabola '''c'''.
| | Drag '''b''' so you can see the vertical movement of parabola '''c'''.
|-
| | Point to '''vertex (a, b)''' for red parabola.
| | Note that as the '''vertex''' is '''a comma b''' for red parabola, the blue parabola does not move at all.
|-
| | Drag '''sliders l''' and '''m'''.

Point to blue parabola.
| | Similarly, let us drag '''l''' and '''m'''.

This only affects the blue parabola.
|-
| | Drag '''slider p''', point to both parabolas.
| | But when we move '''p''', both parabolas are affected.
|-
| | Drag '''sliders a, b, l''' and '''m''' to 0.

Drag '''slider p''' to 1.
| | Drag '''sliders a, p, b, l''' and '''m''' to 0.

Now let us move '''p''' to 1.
|-
| | Point to the red and blue parabolas in '''Graphics''' view.
| | Note the effects on the parabolas’ graphs and equations in '''Graphics''' and '''Algebra''' views.
|-
| |
| | 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.
|-
|}

@@ Line 29: / Line 29: @@
-   www.spoken-tutorial.org
+www.spoken-tutorial.org
 ||To follow this '''tutorial''', you should have basic knowledge of
 '''GeoGebra''' interface

@@ Line 17: / Line 17: @@
 * Construct parabolas.
 |-
-||'''Slide Number 3'''
+|| '''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'''
@@ Line 31: / Line 24: @@
 '''GeoGebra 5.0.388.0-d'''
 |-
 ||'''Slide Number 5'''
@@ Line 39: / Line 44: @@
 The points on the parabola are also equidistant from the fixed line called the '''directrix'''.
-||Parabola.
+||Parabola
 A parabola is the '''locus''' of points equidistant from the fixed point called the focus.
@@ Line 115: / Line 120: @@
 Type '''axis of symmetry''' in '''New Name''' field.
-Click '''OK'''
+Click '''OK'''.
 |-
 ||Click on '''Parabola''' tool under '''Ellipse''' tool.
@@ Line 240: / Line 245: @@
 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'''.
 |-

@@ Line 39: / Line 39: @@
 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.
+||Parabola.
 The points on the parabola are also equidistant from the fixed line called the '''directrix'''.
@@ Line 54: / Line 56: @@
 I have already opened '''GeoGebra''' interface.
 |-
-||Click on '''Point''' tool and click in '''Graphics''' view.
+||Click on '''Point''' tool >> click in '''Graphics''' view.
 Point to point '''A'''.
@@ Line 399: / Line 401: @@
 '''Assignment'''
-Find the coordinates of the '''foci''' and length of '''latus recti''' for these parabolas.
+Find the coordinates of the '''foci''' >> length of '''latus recti''' for these parabolas.
 Also, find the equations of the '''axes of symmetry''' and '''directrices'''.

@@ Line 369: / Line 369: @@
 |  | For parabola '''c''', '''Focus''', '''Vertex''' and '''Directrix''' and their '''coordinates''' and equation appear red.
 |-
-|  |Follow the earlier steps to construct parabola '''d'''.
+|  |Show '''Geogebra''' window with parabolas '''c''' and '''d'''.
 |  |Follow the earlier steps to construct parabola '''d'''.
 |-

@@ Line 347: / Line 347: @@
 |  | The equation for the '''Directrix''' of parabola '''c''', '''y equals 0''', appears in '''Algebra''' view.
 |-
-|  | Double click on '''Directrix''' in '''Graphics''' view >> '''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.
-Choose '''Object Properties''', then the '''Color''' tab.
+In the '''Redefine''' text box, click on '''Object Properties''', then on the '''Color''' tab.
 |-
 |  | In the left panel, point to highlighted '''Directrix''', identify '''Focus''' and ''' Vertex''' created for parabola '''c'''.
@@ Line 369: / Line 369: @@
 |  | For parabola '''c''', '''Focus''', '''Vertex''' and '''Directrix''' and their '''coordinates''' and equation appear red.
 |-
 |  |Follow the earlier steps to construct parabola '''d'''.
+|  |Follow the earlier steps to construct parabola '''d'''.
-In '''input bar''', type '''y minus l in parentheses caret 2 equals 4 space p space x minus m in parentheses'''.
-−
-'''l comma m''' correspond to the '''co-ordinates''' of the '''vertex'''.
-−
-Set '''sliders l''' and '''m''' at 2 and '''p''' at 1.
-−
-Equation '''d''' is given by '''y squared minus 4x minus 4y minus 12'''.
-−
-Note the effects of '''sliders a, p, b, l''' and '''m''' on the parabolas.
-−
-Find the '''focus, vertex''' and '''directrix''' for parabola '''d'''.
 |-
 |  |