Write an equation for the hyperbola.
-vertices at $( 5,0 ) , ( - 5,0 )$; foci at $( 9,0 ) , ( - 9,0 )$
A) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 81 } = 1$

B) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 56 } = 1$

C) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 25 } = 1$

D) $\frac { x ^ { 2 } } { 56 } - \frac { y ^ { 2 } } { 25 } = 1$

Question

Write an equation for the hyperbola.
-vertices at $( 5,0 ) , ( - 5,0 )$; foci at $( 9,0 ) , ( - 9,0 )$
A) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 81 } = 1$

B) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 56 } = 1$

C) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 25 } = 1$

D) $\frac { x ^ { 2 } } { 56 } - \frac { y ^ { 2 } } { 25 } = 1$

Quizplus · Accepted Answer

The vertices and foci indicate a horizontal hyperbola centered at the origin. The distance from the center to a vertex is 5, so $a^2 = 25$. The distance from the center to a focus is 9, so $c^2 = 81$. Using $c^2 = a^2 + b^2$, we find $b^2 = 56$. Thus, the equation is $\frac{x^2}{25} - \frac{y^2}{56} = 1$.

Write an Equation for the Hyperbola (5,0),(−5,0)( 5,0 ) , ( - 5,0 )(5,0),(−5,0)

Write an Equation for the Hyperbola $( 5,0 ) , ( - 5,0 )$