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

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 $y = - 3 x$

Quizplus · Accepted Answer

The asymptotes of a hyperbola given by the equation $y^2 - x^2 = 9$ are found by setting the right side equal to zero, which gives $y^2 - x^2 = 0$, or $y^2 = x^2$. Taking the square root of both sides gives the equations of the asymptotes as $y = x$ and $y = -x$.

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

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