Hyperbola Graphing Recall that the equations for a
Hyperbola - Graphing • Recall that the equations for a hyperbola are. . . Horizontal Axis Vertical Axis Table of Contents
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). Table of Contents Slide 2
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. Table of Contents Slide 3
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 Table of Contents 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. Table of Contents 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. . . Table of Contents © 2000 Alan J. Dinwiddie, Jerry C. Neve Slide 4
Hyperbola - Graphing • As Sketch Now Plot Draw Use athe two last plot diagonals the four vertices more step, the center points vertices the points through and at foci to C(-4, the badraw can ==asymptotes the 351) be units acorners. . . rectangle plotted to above the to of. . . sketch left the. . . andbox. and below the right These theof center the lines hyperbola center form. . . asymptotes for the hyperbola. . . 12 F (V 4(-, 41 , +6) 34 ) C (- 4, 1) -8 8 4 -4 FV (- (4 , 41, –- 4) 34 ) Table of Contents -8 Slide 4
Hyperbola - Graphing Table of Contents
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