ApplicationsofGeoGebra/C2/ConicSectionsParabola/Englishtimed
From Script  SpokenTutorial
Time  Narration 
00:01  Welcome to this tutorial on Conic Sections Parabola. 
00:06  In this tutorial, we will learn how to use GeoGebra to: 
00:11  Study standard equations and parts of a parabola 
00:16  Construct parabolas. 
00:19  Here I am using:
Ubuntu Linux Operating System version 14.04, GeoGebra 5.0.388.0 hyphen d 
00:33  To follow this tutorial, you should have basic knowledge of
GeoGebra interface, Conic sections in geometry 
00:42  For relevant tutorials, please visit our website. 
00:46  Parabola
A parabola is the locus of points equidistant from the fixed point called the focus. 
00:57  The points on the parabola are also equidistant from the fixed line called the directrix. 
01:05  Observe the different features of the parabola in the image. 
01:10  The Axis of Symmetry is perpendicular to the Directrix and passes through the Focus and Vertex. 
01:19  Latus Rectum passes through the Focus and is perpendicular to the Axis of Symmetry. 
01:27  Let us construct a parabola in GeoGebra. 
01:31  I have already opened GeoGebra interface. 
01:35  Click on Point tool and click in Graphics view.
This creates point A. 
01:44  Rightclick on point A and select the Rename option. 
01:49  In the New Name text box, type Focus instead of A and click OK. 
01:57  This renames point A as Focus. 
02:01  Click on Line tool and click on two places in Graphics view, below Focus. 
02:10  This creates line AB. 
02:14  Rightclick on line AB and choose the Rename option. 
02:20  In the New Name field, type directrix and click OK. 
02:28  This renames line AB as the directrix. 
02:33  Click on Perpendicular Line tool, then click on line AB. 
02:41  Drag the cursor until the resulting line passes through Focus and click on Focus. 
02:51  This draws a line perpendicular to line AB, passing through Focus.

03:01  Rightclick on this line perpendicular to line AB. 
03:07  Choose the Rename option. 
03:10  Type axis of symmetry in New Name field.
Click OK. 
03:19  Under Ellipse tool, click on Parabola tool. 
03:25  Then click on Focus and the directrix. 
03:31  This creates a parabola with its focus at Focus and with line AB as the directrix. 
03:39  Under Point tool, click on Intersect tool. 
03:44  Click on the parabola and axis of symmetry. 
03:50  This creates point C at the intersection. 
03:54  It is the vertex of the parabola. 
03:58  Rightclick on point C and choose the Rename option. 
04:04  In the New Name field, type Vertex and click OK. 
04:10  Click on Perpendicular Line tool and click on the axis of symmetry. 
04:18  Drag the cursor until the line passes through the Focus and click on it. 
04:24  This results in a line parallel to the directrix, passing through the Focus. 
04:31  Under Point tool, click on Intersect tool. 
04:35  Click on the parabola and the newly drawn line through Focus. 
04:42  This creates points C and D. 
04:46  Under Line tool, click on Segment tool and click on points C and D. 
04:55  Resulting Segment CD is the latus rectum. 
04:59  Rightclick on Segment CD and choose the Rename option. 
05:05  In the New Name field, type Latus Rectum and click OK. 
05:13  Move the Latus label so you can see it properly. 
05:18  Click and drag Graphics view to see the parabola properly. 
05:24  In Algebra view, you can see the equation describing the parabola. 
05:30  Drag boundary so you can see the equation properly. 
05:35  Also, you can see the equations for the axis of symmetry, directrix and latus rectum. 
05:43  Drag boundary so you can see Graphics view properly again. 
05:49  Click in Graphics view and drag background. 
05:54  Under Point tool, click on Intersect tool. 
05:59  Click on axis of symmetry and directrix. 
06:05  This creates point E. 
06:08  Under Angle tool, click on Distance or Length tool. 
06:13  Click on Focus and Vertex. 
06:18  Note the distance of FocusVertex appearing in Graphics view. 
06:23  Click on Vertex and point E. 
06:27  Note the distance of Vertex E appearing in Graphics view.
Both these distances are equal. 
06:36  Let us look at the general equations of parabolas. 
06:41  I have opened a new GeoGebra window. 
06:45  In input bar, type x minus a in parentheses caret 2 equals 4 space p space y minus b in parentheses. 
07:02  To type caret symbol, hold Shift key down and press 6. 
07:09  Note that the spaces denote multiplication.
Press Enter. 
07:16  Create Sliders window pops up asking if you want to create sliders for a, b and p. 
07:24  Click on Create Sliders. 
07:27  Sliders are created for a, p and b. 
07:32  The default setting for all three coefficients is 1. 
07:36  A parabola opening upwards appears in Graphics view. 
07:41  a comma b correspond to the coordinates of the vertex. 
07:47  Double click on the parabola, click on Object Properties and then on Color tab. 
07:56  Select red and close the Preferences box. 
08:00  The parabola and its equation appear red in the Graphics and Algebra views. 
08:08  Move boundary so you can see the equation properly. 
08:13  Right click on slider a and check Animation On option. 
08:19  Note the effects on the horizontal movement of the red parabola. 
08:24  Rightclick on slider a and uncheck Animation On option. 
08:30  Rightclick on slider p and check Animation On option. 
08:35  Note the effects on the shape and orientation of the parabola. 
08:40  Rightclick on slider p and uncheck Animation On option. 
08:46  Rightclick on slider b and check Animation On option. 
08:52  Note the effects on the vertical movement of the parabola. 
08:57  Rightclick on slider b and uncheck Animation On option. 
09:03  Note that when a, p and b are equal to 1, the red parabola c is described by equation c. 
09:16  Click on parabola c in Graphics view and note highlighting of equation c in Algebra view. 
09:25  Equation c is given by x squared minus 2x minus 4y equals minus 5. 
09:33  In input bar, type Focus c in parentheses.
Press Enter. 
09:41  Focus is drawn at point A in Graphics view. 
09:46  The coordinates of Focus of parabola c, which is point A, appear in Algebra view. 
09:53  In input bar, type Vertex c in parentheses.
Press Enter. 
10:01  Vertex is drawn at point B in Graphics view. 
10:05  The coordinates of Vertex of parabola c, which is point B, appear in Algebra view. 
10:12  In input bar, type Directrix c in parentheses.
Press Enter. 
10:21  Directrix appears as a line along x axis in Graphics view. 
10:26  The equation for the Directrix of parabola c, y equals 0, appears in Algebra view. 
10:34  Double click on Directrix in Graphics view. 
10:38  In the Redefine text box, click on Object Properties, then the Color tab. 
10:45  In the left panel, note that the Directrix is highlighted. 
10:51  Identify Focus and Vertex created for parabola c. 
10:56  While pressing the Control key, click and highlight Focus and Vertex. 
11:03  Click on red. 
11:06  Close the Preferences box. 
11:09  For parabola c, Focus, Vertex and Directrix and their coordinates and equation appear red. 
11:19  Follow the earlier steps to construct parabola d. 
11:24  Let us summarize. 
11:26  In this tutorial, we have learnt how to use GeoGebra to:
Study the standard equations and parts of a parabola, Construct parabolas 
11:36  As an assignment:
Try these steps to construct parabolas with these foci and directrices. 
11:45  Find their equations. 
11:47  As an assignment: Find the coordinates of the foci and length of the latus recti for these parabolas. 
11:56  Also, find the equations of the axes of symmetry and directrices. 
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