Find an equation in standard form for the hyperbola that satisfies the given conditions.
-Vertices at $( \pm 3,0 )$, foci at $( \pm 9,0 )$
A) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 81 } = 1$
B) $\frac { x ^ { 2 } } { 72 } - \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 72 } = 1$

Question

Quizplus · Accepted Answer

The standard form of a horizontal hyperbola is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, where $2a$ is the distance between the vertices, and $c$ is the distance from the center to a focus. Given vertices at $(\pm 3,0)$, we have $a=3$, so $a^2=9$. The distance from the center to a focus is $c=9$, so $c^2=81$. Using $c^2=a^2+b^2$, we find $b^2=c^2-a^2=81-9=72$. Thus, the equation is $\frac{x^2}{9} - \frac{y^2}{72} = 1$.

Find an Equation in Standard Form for the Hyperbola That (±3,0)( \pm 3,0 )(±3,0)

Find an Equation in Standard Form for the Hyperbola That $( \pm 3,0 )$