Find the vertices and asymptotes of the hyperbola. $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 1$
A)vertices: (0, ±8) asymptote: y = ± $\frac { 9 } { 8 }$ x
B)vertices: (0, ±8) asymptote: y = ± $\frac { 8 } { 9 }$ x
C)vertices: (±8, 0) asymptote: y = ± $\frac { 9 } { 8 }$ x
D)vertices: (±8, 0) asymptote: y = ± $\frac { 8 } { 9 }$ x
E)vertices: (±8, 9) asymptote: y = ± $\frac { 8 } { 9 }$ x

Question

Quizplus · Accepted Answer

The given equation is of the form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, which is a hyperbola centered at the origin with vertices along the x-axis. Here, $a^2 = 64$ and $b^2 = 81$, so $a = 8$ and $b = 9$. The vertices are at $(±a, 0)$, which gives $(±8, 0)$. The asymptotes for a hyperbola of this form are given by $y = ±\frac{b}{a}x$, which simplifies to $y = ±\frac{9}{8}x$.

Find the Vertices and Asymptotes of the Hyperbola x264−y281=1\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 164x2​−81y2​=1

Find the Vertices and Asymptotes of the Hyperbola $\frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 81 } = 1$