Write an equation for the hyperbola.
-vertices at $( 0 , \pm 10 )$, asymptotes at $y = \pm \frac { 5 } { 4 } x$
A) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 25 } = 1$

B) $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 64 } = 1$

C) $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 16 } = 1$

D) $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 100 } = 1$

Question

Write an equation for the hyperbola.
-vertices at $( 0 , \pm 10 )$, asymptotes at $y = \pm \frac { 5 } { 4 } x$
A) $\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 25 } = 1$

B) $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 64 } = 1$

C) $\frac { y ^ { 2 } } { 100 } - \frac { x ^ { 2 } } { 16 } = 1$

D) $\frac { y ^ { 2 } } { 64 } - \frac { x ^ { 2 } } { 100 } = 1$

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 for a vertical hyperbola is given by $\pm \frac{a}{b}$, so from $y = \pm \frac{5}{4}x$, we find $b = 8$ and $b^2 = 64$. Thus, the correct equation is $\frac{y^2}{100} - \frac{x^2}{64} = 1$.

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

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