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

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	Right-click 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	Right-click 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. This line is the axis of symmetry.
03:01	Right-click 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	Right-click 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	Right-click 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 co-ordinates 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	Right-click on slider a and uncheck Animation On option.
08:30	Right-click on slider p and check Animation On option.
08:35	Note the effects on the shape and orientation of the parabola.
08:40	Right-click on slider p and uncheck Animation On option.
08:46	Right-click on slider b and check Animation On option.
08:52	Note the effects on the vertical movement of the parabola.
08:57	Right-click 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.
12:03	The video at the following link summarizes the Spoken Tutorial Project. Please download and watch it.
12:11	The Spoken Tutorial Project team conducts workshops and gives certificates. For more details, please write to us.
12:20	Please post your timed queries on this forum.
12:24	Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. More information on this mission is available at this link.
12:37	This is Vidhya Iyer from IIT Bombay, signing off. Thank you for joining.

Contributors and Content Editors

PoojaMoolya