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

Time	Narration
00:01	Welcome to this tutorial on Conic Sections - Hyperbola.
00:06	In this tutorial, we will: Study standard equations and parts of hyperbolae
00:13	Learn how to use GeoGebra to construct a hyperbola.
00:18	Here I am using: Ubuntu Linux OS version 14.04 , GeoGebra 5.0.388.0 hyphen d
00:33	To follow this tutorial, you should be familiar with GeoGebra interface
00:40	Conic Sections in geometry
00:43	For relevant tutorials, please visit our website.
00:48	Hyperbola, Consider two fixed points F1 and F2 called foci.
00:57	A hyperbola is the locus of points whose difference of distances from these foci is constant.
01:07	In the image, observe that foci of a hyperbola lie along the transverse axis.
01:15	They are equidistant from the center which lies on the conjugate axis.
01:22	2b is the length of the conjugate axis.
01:27	c is the distance of each focus from the center.
01:33	The conjugate axis is perpendicular to the transverse axis.
01:38	The hyperbola intersects the transverse axis at the vertices A and B.
01:46	a is the distance of each vertex from the center.
01:52	The latus recti pass through the foci.
01:56	They are perpendicular to the transverse axis.
02:00	Be careful to distinguish lengths from letters used for sliders, circles and hyperbolae.
02:08	Let us construct a hyperbola in GeoGebra.
02:13	I have already opened the GeoGebra interface.
02:18	Click on Point tool and click twice in Graphics view.
02:26	This creates two points A and B, which will be the foci of our hyperbola.
02:33	Right-click on A and choose the Rename option.
02:39	In the New Name field, type F1 and click OK.
02:45	This will be one of our foci, F1.
02:49	Let us rename point B as F2.
02:53	Click on Slider tool and click in Graphics view.
03:00	A Slider dialog-box appears in Graphics view.
03:04	Stay with the default Number selection.
03:08	In the Name field, type k.
03:12	Set Min value as 0, Max value as 10, increment as 0.1, click OK.
03:26	This creates a number slider named k.
03:30	Using this slider, k can be changed from 0 to 10.
03:36	k will be the difference of the distances of any point on the hyperbola from the foci, F1 and F2.
03:45	Drag slider k to 4.
03:49	We will create another number slider named a.
03:54	Its Min value is 0, Max value is 25,increment is 0.1.
04:02	Click on Circle with Center and Radius tool and click on F1.
04:10	A text-box appears; type a and click OK.
04:17	Drag a to a value between 2 and 3.
04:23	A circle c with center F1 and radius a appears.
04:29	Drag slider a to 5.
04:33	Under Move Graphics View, click on Zoom Out tool.
04:39	Click in Graphics view.
04:42	Click on Move Graphics View to move the background as required.
04:48	Click again on Circle with Center and Radius tool and click on F2.
04:56	In the text-box, type a minus k and click OK.
05:03	Circle d with center F2 and radius a minus k appears.
05:10	Click again on Circle with Center and Radius tool and click on F2.
05:18	In the text-box, type a plus k and click OK.
05:25	Circle e with center F2 and radius a plus k appears.
05:32	Set slider k between 1 and 2, slider a between 3 and 4.
05:40	Under Point, click on Intersect.
05:46	Then click on circles c and d and circles c and e.
05:55	This creates points A, B, C and D.
06:05	Under Line, click on Segment and click on points A and F1 to join them.
06:15	Then click on points A and F2 to join them.
06:21	Similarly, using Segment tool, join B and F1 as well as B and F2.
06:31	Click on Move.
06:34	Double click on segment AF1 and click on Object Properties.
06:42	In the left panel, segment AF1 is already highlighted.
06:48	Holding Ctrl Key down, click and highlight segments AF2, BF1 and BF2.
06:58	Under the Basic tab, make sure Show Label is checked.
07:03	Choose Name and Value from the dropdown menu next to it.
07:08	Under the Color tab, select red.
07:12	Under the Style tab, select dashed line style.
07:17	Close the Preferences box.
07:20	Click on Move if it is not highlighted.
07:24	Move the labels to see them properly in Graphics view.
07:30	Now, let us carry out the same steps for segments CF1, CF2, DF1 and DF2 but make them blue.
07:39	Click on Move if it is not highlighted.
07:42	And move the labels to see them properly in Graphics view.
07:49	Right-click on points A, B, C and D and select Trace On option.
08:03	Set slider k at 1.
08:07	Drag slider a to both ends of the slider.
08:12	Set first k at 2.
08:17	Then at 3.
08:21	At 5.
08:24	And finally at 10.
08:28	Observe the traces of hyperbolae for the different values of a and k
08:34	Let us look at the equations of hyperbolae.
08:38	Open a new GeoGebra window.
08:41	In the input bar, type the following line describing the difference of two fractions equal to 1.
08:48	To type the caret symbol, hold the Shift key down and press 6.
08:53	For the 1st fraction, type the numerator as x minus h in parentheses caret 2. Then type division slash.
09:03	Now, type the denominator of the 1st fraction as a caret 2 followed by minus.
09:11	For the 2nd fraction, type the numerator as y minus k in parentheses caret 2. Then type division slash.
09:01	Now, type the denominator of the 2nd fraction as b caret 2 followed by equals sign 1. Press Enter.
09:31	A pop-up window asks if you want to create sliders for a, b, h and k.
09:38	Click on Create Sliders.
09:41	This creates number sliders for h, a, k and b.
09:48	By default, they go from minus 5 to 5 and are set at 1.
09:54	You can double-click on the sliders to see their properties.
09:58	A hyperbola appears in Graphics view.
10;02	Under Move Graphics View, click on Zoom Out and then in Graphics view.
10:11	Click on Move Graphics View and drag Graphics view to see the hyperbola properly.
10:20	In Algebra view, note the equation for hyperbola c.
10:25	Drag the boundary to see it properly.
10:29	Keep track of the equations appearing in Algebra view as you drag the sliders from end to end.
10:36	You will see the effects on the shape of hyperbola c.
10:41	Place the cursor over the equation in Algebra view.
10:46	Note that a is associated with the x minus h squared component of the equation.
10:53	It controls the horizontal movement of hyperbola c.
11:00	Associated with the y minus k squared component is b.
11:06	It controls the vertical movement of hyperbola c.
11:12	Note that the transverse axis of hyperbola c is horizontal like the x axis.
11:19	Drag slider a to 2, leaving b at 1.
11:25	When a is greater than b, the arms of the hyperbola are closer to the x axis.
11:32	Note the equation of the hyperbola.
11:36	Drag the boundary to see it properly.
11:39	With slider a at 2, drag slider b to 3.
11:44	When a is less than b, the arms of the hyperbola stretch closer to the y axis.
11:52	Note the equation of hyperbola c.
11:56	Drag the boundary to see it properly.
12:00	With slider a at 2, drag slider b back to 1.
12:06	Click in and drag Graphics view to see the hyperbola properly.
12:12	In the input bar, type Focus c in parentheses and press Enter.
12:20	Two foci, A and B, are mapped in Graphics view.
12:25	Their coordinates appear in Algebra view.
12:29	In the input bar, type Center c in parentheses and press Enter.
12:37	Center, point C, appears in Graphics view.
12:42	Its co-ordinates appear in Algebra view.
12:46	Note that the center has the coordinates h comma k.
12:52	Drag sliders h and k from end to end.
12:59	Note the effects on hyperbola c.
13:02	In the input bar, type Vertex c in parentheses and press Enter.
13:11	Vertices, D and E, appear on hyperbola c.
13:17	Let us drag a so we can see the vertices clearly.
13:23	Drag the boundary to see Graphics view properly.
13:28	Click in Graphics view and drag the background so you can see the hyperbola properly.
13:34	Drag slider a back to 2.
13:38	Under Slider, click on Text and click in Graphics view.
13:45	A text-box opens up. In the Edit field, type the following text.
13:52	Press Enter after each line to go to the next line and Click OK.
13:58	Refer to additional material provided with this tutorial for these calculations.
14:05	Click on Move Graphics View and drag the background so you can see the hyperbola.
14:13	Uncheck equation c and all points and text generated for hyperbola c in Algebra view.
14:25	Follow the earlier steps to construct hyperbola d for these two conditions.
14:32	Let us summarize.
14:34	In this tutorial, we have learnt how to use GeoGebra to: Construct a hyperbola
14:41	Look at standard equations and parts of hyperbolae
14:45	As an assignment, Find all these values.
14:53	Find all these values for these hyperbolae.
15:00	The video at the following link summarizes the Spoken Tutorial project. Please download and watch it.
15:08	The Spoken Tutorial Project team conducts workshops and gives certificates. For more details, please write to us.
15:17	Please post your timed queries on this forum.
15:21	Spoken Tutorial Project is funded by NMEICT, MHRD, Government of India. More information on this mission is available at this link.
15:34	This is Vidhya Iyer from IIT Bombay, signing off. Thank you for joining.

Contributors and Content Editors

PoojaMoolya