Determine the equations of the asymptotes for the equation.
-$y ^ { 2 } - x ^ { 2 } = 16$
A) $y = \pm \frac { 1 } { 4 } x$
B) $y = \pm 4 x$
C) $y = \pm x$
D) $y = \pm \frac { 1 } { 16 } x$

Question

Quizplus · Accepted Answer

The equation $y^2 - x^2 = 16$ can be rewritten in the form $\frac{y^2}{16} - \frac{x^2}{16} = 1$, which is a hyperbola centered at the origin. The asymptotes of a hyperbola given by $\frac{y^2}{a^2} - \frac{x^2}{b^2} = 1$ are $y = \pm \frac{a}{b}x$. Here, $a^2 = b^2 = 16$, so $a = b = 4$, and the asymptotes are $y = \pm \frac{4}{4}x$, which simplifies to $y = \pm x$.

Determine the Equations of the Asymptotes for the Equation y2−x2=16y ^ { 2 } - x ^ { 2 } = 16y2−x2=16

Determine the Equations of the Asymptotes for the Equation $y ^ { 2 } - x ^ { 2 } = 16$