PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this '''tutorial''' on '''Conic Sections Parabola'''. |- ||00:06 ||In this '''tutorial''', we will learn h..."

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Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this '''tutorial''' on '''Conic Sections Parabola'''. |- ||00:06 ||In this '''tutorial''', we will learn h..."

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{|border=1
||'''Time'''
||'''Narration'''

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||00:01
||Welcome to this '''tutorial''' on '''Conic Sections Parabola'''.

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||00:06
||In this '''tutorial''', we will learn how to use '''GeoGebra''' to:

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||Study standard equations and parts of a parabola

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|| Construct parabolas.

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||Here I am using:

'''Ubuntu Linux''' Operating System version 14.04, '''GeoGebra 5.0.388.0 hyphen d'''
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||00:33
||To follow this '''tutorial''', you should have basic knowledge of

'''GeoGebra''' interface, '''Conic sections''' in geometry

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||For relevant tutorials, please visit our website.
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||00:46
||Parabola

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

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

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||Observe the different features of the parabola in the image.

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

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||'''Latus Rectum''' passes through the Focus and is perpendicular to the '''Axis of Symmetry'''.
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||Let us construct a parabola in '''GeoGebra'''.

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|| 01:31
||I have already opened '''GeoGebra''' interface.
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||01:35
||Click on '''Point''' tool and click in '''Graphics''' view.

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

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||This renames point '''A''' as '''Focus'''.
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||Click on '''Line''' tool and click on two places in '''Graphics''' view, below '''Focus'''.

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||This creates line '''AB'''.
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||Right-click on line '''AB''' and choose the '''Rename''' option.
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||In the '''New Name''' field, type '''directrix''' and click '''OK'''.

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||This renames line '''AB''' as the '''directrix'''.
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||Click on '''Perpendicular Line''' tool, then click on line '''AB'''.
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||Drag the '''cursor''' until the resulting line passes through '''Focus''' and click on '''Focus'''.
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||This draws a line perpendicular to line '''AB''', passing through '''Focus'''.

This line is the '''axis of symmetry'''.
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||Right-click on this line perpendicular to line '''AB'''.

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||Choose the '''Rename''' option.

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||Type '''axis of symmetry''' in '''New Name''' field.

Click '''OK'''.
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||Under '''Ellipse''' tool, click on '''Parabola''' tool.

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||Then click on '''Focus''' and the '''directrix'''.
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||This creates a parabola with its focus at '''Focus''' and with line '''AB''' as the '''directrix'''.
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||Under '''Point''' tool, click on '''Intersect''' tool.

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||Click on the parabola and '''axis of symmetry'''.
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||This creates point '''C''' at the intersection.

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||It is the '''vertex''' of the parabola.
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||Right-click on point '''C''' and choose the '''Rename ''' option.
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||In the '''New Name''' field, type '''Vertex''' and click '''OK'''.
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||Click on '''Perpendicular Line''' tool and click on the '''axis of symmetry'''.
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||Drag the '''cursor''' until the line passes through the '''Focus''' and click on it.
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||This results in a line parallel to the '''directrix''', passing through the '''Focus'''.
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||Under '''Point''' tool, click on '''Intersect''' tool.

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||Click on the parabola and the newly drawn line through '''Focus'''.
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||This creates points '''C''' and '''D'''.
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||Under '''Line''' tool, click on '''Segment''' tool and click on points '''C''' and '''D'''.
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||Resulting Segment '''CD''' is the '''latus rectum'''.
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||Right-click on Segment '''CD''' and choose the '''Rename''' option.
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||In the '''New Name''' field, type '''Latus Rectum''' and click '''OK'''.
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||Move the '''Latus''' label so you can see it properly.
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||Click and drag '''Graphics''' view to see the parabola properly.
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||In '''Algebra''' view, you can see the equation describing the parabola.

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||Drag boundary so you can see the equation properly.

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||Also, you can see the equations for the '''axis of symmetry, directrix''' and '''latus rectum'''.
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||Drag boundary so you can see '''Graphics''' view properly again.
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||Click in '''Graphics''' view and drag background.
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||Under '''Point''' tool, click on '''Intersect''' tool.

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||Click on '''axis of symmetry''' and '''directrix'''.
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||This creates point '''E'''.
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||Under '''Angle''' tool, click on '''Distance or Length''' tool.
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||Click on '''Focus''' and '''Vertex'''.
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||Note the distance of '''FocusVertex''' appearing in '''Graphics''' view.
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||Click on '''Vertex''' and point '''E'''.
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||Note the distance of '''Vertex E''' appearing in '''Graphics''' view.

Both these distances are equal.
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||06:36
||Let us look at the general equations of parabolas.
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||06:41
||I have opened a new '''GeoGebra''' window.
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||In '''input bar''', type '''x minus a in parentheses caret 2 equals 4 space p space y minus b''' in parentheses'''.

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

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||Note that the spaces denote multiplication.

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

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||The '''default''' setting for all three '''coefficients''' is 1.
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||A parabola opening upwards appears in '''Graphics''' view.

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||'''a comma b''' correspond to the '''co-ordinates''' of the '''vertex'''.
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||Double click on the parabola, click on '''Object Properties''' and then on '''Color''' tab.
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||Select red and close the '''Preferences''' box.
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||The parabola and its equation appear red in the '''Graphics''' and '''Algebra''' views.
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||Move boundary so you can see the equation properly.
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||Right click on '''slider a''' and check '''Animation On''' option.
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||Note the effects on the horizontal movement of the red parabola.
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||Right-click on '''slider a''' and uncheck '''Animation On''' option.
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||Right-click on '''slider p''' and check '''Animation On''' option.
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||Note the effects on the shape and orientation of the parabola.
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||08:40
||Right-click on '''slider p''' and uncheck '''Animation On''' option.
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||08:46
||Right-click on '''slider b''' and check '''Animation On''' option.
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||08:52
||Note the effects on the vertical movement of the parabola.
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||08:57
||Right-click on '''slider b''' and uncheck '''Animation On''' option.
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||09:03
||Note that when '''a''', '''p''' and '''b '''are equal to 1, the red parabola '''c''' is described by equation '''c'''.

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|| 09:16
||Click on parabola '''c''' in '''Graphics''' view and note highlighting of equation '''c''' in '''Algebra''' view.

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||Equation '''c''' is given by x squared minus 2x minus 4y equals minus 5.
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||09:33
||In '''input bar''', type '''Focus c''' in parentheses.

Press '''Enter'''.

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||'''Focus''' is drawn at point '''A ''' in '''Graphics''' view.
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||The coordinates of '''Focus''' of parabola '''c''', which is point '''A''', appear in '''Algebra''' view.
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||09:53
||In '''input bar''', type '''Vertex c''' in parentheses.

Press '''Enter'''.

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||'''Vertex''' is drawn at point '''B''' in '''Graphics''' view.

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||10:05
||The '''coordinates''' of '''Vertex''' of parabola '''c''', which is point '''B''', appear in '''Algebra''' view.

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||10:12
||In '''input bar''', type '''Directrix c''' in parentheses.

Press '''Enter'''.

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

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||10:26
||The equation for the '''Directrix''' of parabola '''c''', '''y equals 0''', appears in '''Algebra''' view.

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||10:34
||Double click on '''Directrix''' in '''Graphics''' view.

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||In the '''Redefine''' text box, click on '''Object Properties''', then the '''Color''' tab.
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||10:45
||In the left panel, note that the '''Directrix''' is highlighted.

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||Identify '''Focus''' and '''Vertex''' created for parabola '''c'''.
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||While pressing the '''Control''' key, click and highlight '''Focus''' and '''Vertex'''.
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||Click on red.
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||Close the '''Preferences''' box.
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||For parabola '''c''', '''Focus''', '''Vertex''' and '''Directrix''' and their '''coordinates''' and equation appear red.
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||Follow the earlier steps to construct parabola '''d'''.
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||11:24
||Let us summarize.
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||11:26
||In this '''tutorial''', we have learnt how to use '''GeoGebra''' to:

Study the standard equations and parts of a parabola, Construct parabolas
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||11:36
||As an assignment:

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

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||Find their equations.
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||11:47
||As an assignment: Find the coordinates of the '''foci''' and length of the '''latus recti''' for these parabolas.

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|| 11:56
||Also, find the equations of the '''axes of symmetry''' and '''directrices'''.
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||12:03
||The video at the following link summarizes the '''Spoken Tutorial Project'''.

Please download and watch it.
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||12:11
||The '''Spoken Tutorial Project''' team conducts workshops and gives certificates.

For more details, please write to us.
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||12:20
||Please post your timed queries on this forum.
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||12:24
||'''Spoken Tutorial Project''' is funded by NMEICT, MHRD, Government of India.

More information on this mission is available at this link.
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||12:37
||This is '''Vidhya Iyer''' from '''IIT Bombay''', signing off.

Thank you for joining.
|-
|}

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

PoojaMoolya: Created page with "{|border=1 ||'''Time''' ||'''Narration''' |- ||00:01 ||Welcome to this '''tutorial''' on '''Conic Sections Parabola'''. |- ||00:06 ||In this '''tutorial''', we will learn h..."