7.2 video tutorials

8/20/2019 7.2 Video Tutorials

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Lesson 7.2 The Hyperbola

1

A. Geometric Definition of a Hyperbola

B. Hyperbola with Center at the Origin

The graph of the equation of each of the following equations is a hyperbola with center at the origin

and having the given properties.

Equation

2 2

2 2 1

0, 0

x y

a b

a b

2 2

2 2 1

0, 0

y x

a b

a b

Vertices ,0a 0, a

Transverse Axis Horizontal, length 2a Vertical, length 2a

Asymptotesb

y xa

a

y xb

Foci 2 2 2, 0 ,c c a b 2 2 20, ,c c a b

Graphs

A hyperbola is the set of points in the plane, the difference of whose

distances from two fixed points F 1 and F 2 is a constant. These two fixed

points are the foci of the hyperbola.


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2

C. Hyperbola with Center at (h, k )

Find an equation for the hyperbola described . Graph the equation.

1. Center at (0, 0); focus at (0, 5); vertex at (0, 3). Video tutorial

Equation:

Vertices:

Asymptotes:

What’s c?

Foci:

The graph of the equation of each of the following equations is a hyperbola with center at the (h, k)

and having the given properties.

Equation 1

2

2

2

2

b

k y

a

h x

12

2

2

2

b

h x

a

k y

Vertices ),( k ah ),( ak h

Major Axis Horizontal, length 2a Vertical, length 2a

Minor Axis Vertical, length 2b Horizontal, length 2b

Foci 222

),(

bac

k ch

222

),(

bac

ck h

Asymptotes )( h xa

bk y )( h x

b

ak y

http://www.youtube.com/watch?v=qjJlQblcUTk&hd=1http://www.youtube.com/watch?v=qjJlQblcUTk&hd=1http://www.youtube.com/watch?v=qjJlQblcUTk&hd=1


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Find an equation for the hyperbola described . Graph the equation.

2. Focus at (0, 6); vertices at (0, -2) and (0, 2) Video tutorial

3. Vertices at (-4, 0) and (4, 0); asymptote the line y=2x Video tutorial

Equation:

Vertices:

Asymptotes:

What’s c?

Foci:

Equation:

Vertices:

Asymptotes:

What’s c?

Foci:

http://www.youtube.com/watch?v=n_6xHw3ChXQ&hd=1http://www.youtube.com/watch?v=n_6xHw3ChXQ&hd=1http://www.youtube.com/watch?v=s-5wOikJXqE&hd=1http://www.youtube.com/watch?v=s-5wOikJXqE&hd=1http://www.youtube.com/watch?v=s-5wOikJXqE&hd=1http://www.youtube.com/watch?v=n_6xHw3ChXQ&hd=1


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Find the center, transverse axis, vertices, foci and asymptotes. Graph each equation.

4. 1416

22

x y

Video tutorial

5. 164 22

x y Video tutorial

Vertices:

Asymptotes:

What’s c?

Foci:

Vertices:

Asymptotes:

What’s c?

Foci:

http://www.youtube.com/watch?v=IGcwp1Xv10E&hd=1http://www.youtube.com/watch?v=IGcwp1Xv10E&hd=1http://www.youtube.com/watch?v=QCStrCBFD14&hd=1http://www.youtube.com/watch?v=QCStrCBFD14&hd=1http://www.youtube.com/watch?v=QCStrCBFD14&hd=1http://www.youtube.com/watch?v=IGcwp1Xv10E&hd=1


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Find the center, transverse axis, vertices, foci and asymptotes. Graph each equation. 6. 42 22 y x Video tutorial

Vertices:

Asymptotes:

What’s c?

Foci:

http://www.youtube.com/watch?v=8DUFGDi1okY&hd=1http://www.youtube.com/watch?v=8DUFGDi1okY&hd=1http://www.youtube.com/watch?v=8DUFGDi1okY&hd=1


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Write an equation for the hyperbola.

7.

Video tutorial

8.

Video tutorial

http://www.youtube.com/watch?v=nAQ2e_rucpo&hd=1http://www.youtube.com/watch?v=nAQ2e_rucpo&hd=1http://www.youtube.com/watch?v=xbr9wvuRZUI&hd=1http://www.youtube.com/watch?v=xbr9wvuRZUI&hd=1http://www.youtube.com/watch?v=nAQ2e_rucpo&hd=1


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Find an equation for the hyperbola described. Graph the equation.

9. Center at (-3, 1); focus at (-3, 6); vertex at (-3, 4)

Video tutorial

Equation

Vertices:

Asymptotes:

What’s c?

Foci:

http://www.youtube.com/watch?v=jFVhvsS5L94&hd=1http://www.youtube.com/watch?v=jFVhvsS5L94&hd=1http://www.youtube.com/watch?v=jFVhvsS5L94&hd=1


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Find an equation for the hyperbola described. Graph the equation.

10. Focus at (-4, 0); vertices at (-4, 4) and (-4, 2) Video tutorial

Equation

Vertices:

Asymptotes:

What’s c?

Foci:

http://www.youtube.com/watch?v=QfjzzgHxv5U&hd=1http://www.youtube.com/watch?v=QfjzzgHxv5U&hd=1http://www.youtube.com/watch?v=QfjzzgHxv5U&hd=1


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Find the center, transverse axis, vertices, foci, and asymptotes. Graph each!

11.

19

2

4

3 22

x y

Video tutorial

Equation

Vertices:

Asymptotes:

What’s c?

Foci:

http://www.youtube.com/watch?v=hAaT0eASvc4&hd=1http://www.youtube.com/watch?v=hAaT0eASvc4&hd=1http://www.youtube.com/watch?v=hAaT0eASvc4&hd=1


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12. 9394 22 y x Video tutorial

Equation

Vertices:

Asymptotes:

What’s c?

Foci:

http://www.youtube.com/watch?v=T1MqeQrpuhg&hd=1http://www.youtube.com/watch?v=T1MqeQrpuhg&hd=1http://www.youtube.com/watch?v=T1MqeQrpuhg&hd=1


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13. 014422 x y x y Video tutorial

Equation

Vertices:

Asymptotes:

What’s c?

Foci:

http://www.youtube.com/watch?v=jC8gF7uqwSo&hd=1http://www.youtube.com/watch?v=jC8gF7uqwSo&hd=1http://www.youtube.com/watch?v=jC8gF7uqwSo&hd=1


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14. 0192164 22 y x x y Video tutorial

Equation

Vertices:

Asymptotes:

What’s c?

Foci:
http://www.youtube.com/watch?v=bxVDdBBf4Yo&hd=1http://www.youtube.com/watch?v=bxVDdBBf4Yo&hd=1http://www.youtube.com/watch?v=bxVDdBBf4Yo&hd=1

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