1. Hyperbola - Graphing
Recall that the equations for a hyperbola are ...
Horizontal Axis
Vertical Axis

2. The center of the hyperbola is located at the point (h, k) ...
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

3. Hyperbola - Graphing
Note how the position of the a is always with the positive term, and the b is always with the negative term.
Horizontal Axis
Vertical Axis
Also, when the positive term includes x, the axis is horizontal. When the positive term includes y, the axis is vertical.
Slide 3

4. The vertices of the hyperbola are located on the axis ...
Hyperbola - Graphing
The vertices of the hyperbola are located on the axis ...
and are a units from the center. a a
Horizontal Axis
Vertical Axis
Slide 4

5. The foci lie on the axis and are c units from the center where ...
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 5

6. Since the positive term includes the y, the axis is vertical.
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 6

7. Use the four points to draw a rectangle ...
Hyperbola - Graphing
Use the four points to draw a rectangle ...
Draw diagonals through the corners of the box. These lines form asymptotes for the hyperbola ...
As a last step, the foci can be plotted ...
Plot two more points b = 3 units to the left and right of the center ...
Use the vertices and the asymptotes to sketch the hyperbola ...
Now plot the vertices a = 5 units above and below the center ...
Sketch the center at C(-4, 1) ... 4 8 12
- 4
- 8
F (- 4 , 1 + 34 )
V (- 4 , 6)
C (- 4, 1)
V (- 4 , - 4)
F (- 4 , 1 – 34 )
Slide 7

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Hyperbola - Graphing
END OF PRESENTATION
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