$\text { Find an equation of the hyperbola with vertices } ( 0 , - 5 ) , ( 0,5 ) \text { and asymptotes }$ $y = \pm \frac { 1 } { 6 } x$
A) $\frac { y ^ { 2 } } { 25 } - \frac { x ^ { 2 } } { 900 } = 1$
B) $\frac { y ^ { 2 } } { 25 } + \frac { x ^ { 2 } } { 900 } = 1$
C) $\frac { y ^ { 2 } } { 30 } - \frac { x ^ { 2 } } { 5 } = 1$
D) $\frac { y ^ { 2 } } { 5 } + \frac { x ^ { 2 } } { 30 } = 1$
E) $\frac { y ^ { 2 } } { 5 } - \frac { x ^ { 2 } } { 30 } = 1$

Question

Quizplus · Accepted Answer

The vertices at (0, -5) and (0, 5) indicate the hyperbola is vertical, with $a = 5$, so $a^2 = 25$. The slope of the asymptotes $\pm \frac{1}{6}$ gives $b/a = 1/6$, so $b = a/6 = 5/6$, and $b^2 = (5/6)^2 = 25/36 = 900/36$. Thus, the equation is $\frac{y^2}{25} - \frac{x^2}{900} = 1$.

Find an equation of the hyperbola with vertices (0,−5),(0,5) and asymptotes \text { Find an equation of the hyperbola with vertices } ( 0 , - 5 ) , ( 0,5 ) \text { and asymptotes } Find an equation of the hyperbola with vertices (0,−5),(0,5) and asymptotes

$\text { Find an equation of the hyperbola with vertices } ( 0 , - 5 ) , ( 0,5 ) \text { and asymptotes }$