Find an equation for the hyperbola described.
-Vertices at $( 0 , \pm 10 )$; asymptotes at $y = \pm \frac { 5 } { 3 } x$
A) $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 36 } = 1$
B) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$
C) $\frac { y ^ { 2 } } { 36 } - \frac { x ^ { 2 } } { 100 } = 1$
D) $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 9 } = 1$

Question

Quizplus · Accepted Answer

The vertices at $(0, \pm 10)$ indicate that the hyperbola is vertical and the distance from the center to a vertex is 10, so $a = 10$ and $a^2 = 100$. The slope of the asymptotes is $\pm \frac{5}{3}$, which is derived from $\frac{b}{a}$ for a vertical hyperbola, leading to $b = \frac{5}{3}a$. Since $a = 10$, $b = \frac{50}{3}$ and $b^2 = \frac{2500}{9} = 36$. Therefore, the equation is $\frac{y^2}{100} - \frac{x^2}{36} = 1$.

Find an Equation for the Hyperbola Described (0,±10)( 0 , \pm 10 )(0,±10)

Find an Equation for the Hyperbola Described $( 0 , \pm 10 )$