Hyperbola - Graphing

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# Hyperbola - Graphing - PowerPoint PPT Presentation

Hyperbola - Graphing. Recall that the equations for a hyperbola are . Horizontal Axis. Vertical Axis. Hyperbola - Graphing. The center of the hyperbola is located at the point (h, k) . Example 1: Determine the center of the hyperbola given by .

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Presentation Transcript
Hyperbola - Graphing
• Recall that the equations for a hyperbola are ...

Horizontal Axis

Vertical Axis

Hyperbola - Graphing
• The center of the hyperbola is located at the
• point (h, k) ...
• Example 1:
• Determine the center of
• the hyperbola given by ...
• The center is at C(7, -3).

Slide 2

Horizontal Axis

Vertical Axis

Hyperbola - Graphing

• Note how the position of the a is always with the positive term, and the b is always with the negative term.
• Also, when the positive term includes x, the axis is horizontal. When the positive term includes y, the axis is vertical.

Slide 3

a

a

Hyperbola - Graphing

• The vertices of the hyperbola are located on the axis ...

and are a units from the center.

Horizontal Axis

Vertical Axis

Slide 4

Hyperbola - Graphing
• The foci lie on the axis and are c units from the center where ...
• Summary:

The center is at C(h, k).

The vertices are a units from the center on the axis.

The foci are c units from the center on the axis.

• The remaining techniques for graphing a hyperbola will be shown in the next example.

Slide 4

Hyperbola - Graphing
• Example 2:
• Sketch the graph of the
• hyperbola given by ...
• The center is at C(-4, 1).
• Since the positive term includes the y, the axis is vertical.
• The value of c is given by ...

Slide 4

© 2000 Alan J. Dinwiddie, Jerry C. Neve

F (- 4 , 1 + 34 )

F (- 4 , 1 – 34 )

12

8

4

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Hyperbola - Graphing

• Draw diagonals through the corners of the box. These lines form asymptotes for the hyperbola ...
• As a last step, the foci can be plotted ...
• Sketch the center at C(-4, 1) ...
• Now plot the vertices a = 5 units above and below the center ...
• Plot two more points b = 3 units to the left and right of the center ...
• Use the four points to draw a rectangle ...
• Use the vertices and the asymptotes to sketch the hyperbola ...

V (- 4 , 6)

C (- 4, 1)

V (- 4 , - 4)

Slide 4

Hyperbola - Graphing

END OF PRESENTATION

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