1. Table of Contents Hyperbola - Graphing Recall that the equations for a hyperbola are... Horizontal AxisVertical Axis

2. Table of Contents Slide 2 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).

3. Table of Contents Slide 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 AxisVertical Axis Also, when the positive term includes x, the axis is horizontal. When the positive term includes y, the axis is vertical.

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

5. Table of Contents Slide 4 Hyperbola - Graphing The foci lie on the axis and are c units from the center where... Summary: The vertices are a units from the center on the axis. The center is at C(h, k). 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.

6. Table of Contents Slide 4 © 2000 Alan J. Dinwiddie, Jerry C. Neve 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... Table of Contents

7. Slide 4 Hyperbola - Graphing 4 4 8 12 - 4 - 8 - 4- 8 C (- 4, 1) V (- 4, 6) V (- 4, - 4) 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... Draw diagonals through the corners of the box. These lines form asymptotes for the hyperbola... Use the vertices and the asymptotes to sketch the hyperbola... As a last step, the foci can be plotted... F (- 4, 1 +  34 ) F (- 4, 1 –  34 )

8. Table of Contents Hyperbola - Graphing