Find the vertices and asymptotes of the hyperbola.
A)vertices: (0, ±8) asymptote: y = ± x
B)vertices: (0, ±8) asymptote: y = ± x
C)vertices: (±8, 0) asymptote: y = ± x
D)vertices: (±8, 0) asymptote: y = ± x
E)vertices: (±8, 9) asymptote: y = ± x

Question

Find the vertices and asymptotes of the hyperbola. 
A)vertices: (0, ±8) asymptote: y = ± x 
B)vertices: (0, ±8) asymptote: y = ± x 
C)vertices: (±8, 0) asymptote: y = ± x 
D)vertices: (±8, 0) asymptote: y = ± x 
E)vertices: (±8, 9) asymptote: y = ± x

Quizplus · Accepted Answer

The hyperbola is centered at the origin, so the vertices will lie on either the x or y axis. Since the hyperbola has a vertical transverse axis (the y term is positive), the vertices will be on the y axis. The distance from the center to the vertices is the square root of (a squared plus b squared), which in this case is the square root of (64 + 25), or 9.2. Since the center is at the origin, the vertices will be at (0, ±8).

To find the asymptotes, we use the formula y = ±(b/a)x. Plugging in the values of a and b from the equation of the hyperbola, we get y = ±(5/8)x. The correct answer is C.

Find the Vertices and Asymptotes of the Hyperbola