Find the asymptotes of the hyperbola.
-$$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$$
A) $y = \frac { 3 } { 2 } x$ and $y = - \frac { 3 } { 2 } x$
B) $y = \frac { 4 } { 9 } x$ and $y = - \frac { 4 } { 9 } x$
C) $y = \frac { 9 } { 4 } x$ and $y = - \frac { 9 } { 4 } x$
D) $y = \frac { 2 } { 3 } x$ and $y = - \frac { 2 } { 3 } x$

Question

Quizplus · Accepted Answer

The asymptotes of a hyperbola given by $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ are $y = \pm \frac{b}{a}x$. For this hyperbola, $a^2 = 4$ and $b^2 = 9$, so $a = 2$ and $b = 3$, making the asymptotes $y = \pm \frac{3}{2}x$.

Find the Asymptotes of the Hyperbola x24−y29=1\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 14x2​−9y2​=1

Find the Asymptotes of the Hyperbola $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$