Find the asymptotes of the hyperbola.
-$$\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$$

A) $y - 1 = \frac { 5 } { 2 } ( x - 2 )$ and $y - 1 = - \frac { 5 } { 2 } ( x - 2 )$

B) $y - 1 = \frac { 2 } { 5 } ( x - 2 )$ and $y - 1 = - \frac { 2 } { 5 } ( x - 2 )$

C) $y - 2 = \frac { 5 } { 2 } ( x - 1 )$ and $y - 2 = - \frac { 5 } { 2 } ( x - 1 )$

D) $y = \frac { 5 } { 2 } ( x - 2 )$ and $y = - \frac { 5 } { 2 } ( x - 2 )$

Question

Find the asymptotes of the hyperbola.
-$$\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$$

A) $y - 1 = \frac { 5 } { 2 } ( x - 2 )$ and $y - 1 = - \frac { 5 } { 2 } ( x - 2 )$

B) $y - 1 = \frac { 2 } { 5 } ( x - 2 )$ and $y - 1 = - \frac { 2 } { 5 } ( x - 2 )$

C) $y - 2 = \frac { 5 } { 2 } ( x - 1 )$ and $y - 2 = - \frac { 5 } { 2 } ( x - 1 )$

D) $y = \frac { 5 } { 2 } ( x - 2 )$ and $y = - \frac { 5 } { 2 } ( x - 2 )$

Quizplus · Accepted Answer

The asymptotes of a hyperbola in the form $\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$ are given by $y-k = \pm \frac{b}{a}(x-h)$. For the given hyperbola, $h=2$, $k=1$, $a^2=4$ (so $a=2$), and $b^2=25$ (so $b=5$). Thus, the asymptotes are $y-1 = \pm \frac{5}{2}(x-2)$.

Find the Asymptotes of the Hyperbola (x−2)24−(y−1)225=1\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 14(x−2)2​−25(y−1)2​=1

Find the Asymptotes of the Hyperbola $\frac { ( x - 2 ) ^ { 2 } } { 4 } - \frac { ( y - 1 ) ^ { 2 } } { 25 } = 1$