Find the vertices and asymptotes of the hyperbola. $16 y ^ { 2 } - 9 x ^ { 2 } = 144$
A)vertices: (0,±3)asymptote: $y = \pm \frac { 3 } { 4 } x$
B)vertices: (0,±3)asymptote: $y = \pm \frac { 4 } { 3 } x$
C)vertices: (±3,0)asymptote: $y = \pm \frac { 3 } { 4 } x$
D)vertices: (±3,0)asymptote: $y = \pm \frac { 4 } { 3 } x$
E)vertices: (±3,4)asymptote: $y = \pm \frac { 3 } { 4 } x$

Question

Find the vertices and asymptotes of the hyperbola.​ $16 y ^ { 2 } - 9 x ^ { 2 } = 144$ ​
A)​vertices: (0,±3)asymptote: $y = \pm \frac { 3 } { 4 } x$
B)​​vertices: (0,±3)asymptote: $y = \pm \frac { 4 } { 3 } x$
C)​vertices: (±3,0)asymptote: $y = \pm \frac { 3 } { 4 } x$
D)​​vertices: (±3,0)asymptote: $y = \pm \frac { 4 } { 3 } x$
E)​vertices: (±3,4)asymptote: $y = \pm \frac { 3 } { 4 } x$

Quizplus · Accepted Answer

The equation is in the form $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$, so $a^2=16$ and $b^2=9$. Therefore, $a=4$ and $b=3$. The vertices are at $(0,\pm a)=(0,\pm4)$, and the asymptotes are $y=\pm\frac{a}{b}x=\pm\frac{4}{3}x$.

Find the Vertices and Asymptotes of the Hyperbola 16y2−9x2=14416 y ^ { 2 } - 9 x ^ { 2 } = 14416y2−9x2=144

Find the Vertices and Asymptotes of the Hyperbola $16 y ^ { 2 } - 9 x ^ { 2 } = 144$