Find an equation for the hyperbola described.
-Vertices at $( - 7,0 )$ and $( 7,0 )$; foci at $( - 11,0 )$ and $( 11,0 )$
A) $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 121 } = 1$
B) $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 72 } = 1$
C) $\frac { x ^ { 2 } } { 72 } - \frac { y ^ { 2 } } { 49 } = 1$
D) $\frac { x ^ { 2 } } { 121 } - \frac { y ^ { 2 } } { 49 } = 1$

Question

Quizplus · Accepted Answer

The vertices and foci indicate a horizontal hyperbola centered at the origin. The distance between the center and a vertex (a) is 7, so $a^2 = 49$. The distance between the center and a focus (c) is 11, so $c^2 = 121$. For a hyperbola, $c^2 = a^2 + b^2$, so $b^2 = 121 - 49 = 72$. The equation is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, which matches choice B: $\frac{x^2}{49} - \frac{y^2}{72} = 1$.

Find an Equation for the Hyperbola Described (−7,0)( - 7,0 )(−7,0)

Find an Equation for the Hyperbola Described $( - 7,0 )$