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

Question

Quizplus · Accepted Answer

The equation of the hyperbola is given in the form $y^2 - x^2 = 9$, which can be rewritten as $\frac{y^2}{3^2} - \frac{x^2}{3^2} = 1$. The asymptotes for a hyperbola in the form $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$ are $y = \pm \frac{a}{b}x$. Here, $a = b = 3$, so the asymptotes are $y = \pm x$.

Find the Asymptotes of the Hyperbola y2−x2=9y ^ { 2 } - x ^ { 2 } = 9y2−x2=9

Find the Asymptotes of the Hyperbola $y ^ { 2 } - x ^ { 2 } = 9$