Solve the problem.
-The hyperbola $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 1$ is shifted horizontally and vertically to obtain the hyperbola $\frac { ( y - 2 ) ^ { 2 } } { 144 } - \frac { ( x - 3 ) ^ { 2 } } { 256 } = 1$ Find the asymptotes of the new hyperbola.
A) $y - 2 = \pm \frac { 9 } { 16 } ( x - 3 )$
B) $y = \pm \frac { 3 } { 4 } x$
C) $y - 2 = \pm \frac { 3 } { 4 } ( x - 3 )$
D) $y = \pm \frac { 9 } { 16 } x$

Question

Quizplus · Accepted Answer

The asymptotes of a hyperbola of the form $\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1$ are given by $y-k = \pm \frac{a}{b}(x-h)$. For the given hyperbola, $a^2 = 144$ and $b^2 = 256$, so $a = 12$ and $b = 16$. Thus, the asymptotes are $y - 2 = \pm \frac{12}{16}(x - 3)$, simplifying to $y - 2 = \pm \frac{3}{4}(x - 3)$.

Solve the Problem y2144−x2256=1\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 1144y2​−256x2​=1

Solve the Problem $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 1$