Write an equation for the hyperbola.
-$x$-intercepts $( \pm 5,0 )$; center at origin; passing through $( 5 \sqrt { 5 } , 6 )$
A) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { y ^ { 2 } } { 9 } - \frac { x ^ { 2 } } { 25 } = 1$
D) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 25 } = 1$

Question

Quizplus · Accepted Answer

The hyperbola has x-intercepts at $( \pm 5,0 )$, so $a^2 = 25$. The equation is $\frac{x^2}{25} - \frac{y^2}{b^2} = 1$. Substituting $(5\sqrt{5}, 6)$ into the equation gives $b^2 = 9$.

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