Find the vertices and asymptotes of the hyperbola.
$$9 y ^ { 2 } - 4 x ^ { 2 } = 36$$
A) vertices: $( 0 , \pm 2 )$ asymptote: $y = \pm \frac { 2 } { 3 } x$
B) vertices: $( 0 , \pm 2 )$ asymptote: $y = \pm \frac { 3 } { 2 } x$
C) vertices: $( \pm 2,0 )$ asymptote: $y = \pm \frac { 2 } { 3 } x$
D) vertices: $( \pm 2,0 )$ asymptote: $y = \pm \frac { 3 } { 2 } x$
E) vertices: $( \pm 2,3 )$ asymptote: $y = \pm \frac { 2 } { 3 } x$

Question

Quizplus · Accepted Answer

The given equation is $9y^2 - 4x^2 = 36$, which can be rewritten as $\frac{y^2}{4} - \frac{x^2}{9} = 1$, indicating a hyperbola centered at the origin with a vertical transverse axis. The vertices are found at $(0, \pm 2)$ because they are $\pm b$ units from the center along the y-axis, where $b^2 = 4$. The asymptotes are given by $y = \pm \frac{b}{a}x$, where $a^2 = 9$, so $y = \pm \frac{2}{3}x$.

Find the Vertices and Asymptotes of the Hyperbola 9y2−4x2=369 y ^ { 2 } - 4 x ^ { 2 } = 369y2−4x2=36

Find the Vertices and Asymptotes of the Hyperbola $9 y ^ { 2 } - 4 x ^ { 2 } = 36$