Write an equation for the hyperbola.
-vertices at $( 4,0 ) , ( - 4,0 )$; foci at $( 5,0 ) , ( - 5,0 )$
A) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 25 } - \frac { y ^ { 2 } } { 16 } = 1$
D) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 9 } = 1$

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 4, so $a^2 = 16$. The distance from the center to a focus (c) is 5, so $c^2 = 25$. For a hyperbola, $c^2 = a^2 + b^2$, solving for $b^2$ gives $b^2 = 9$. Thus, the equation is $\frac{x^2}{16} - \frac{y^2}{9} = 1$.

Write an Equation for the Hyperbola (4,0),(−4,0)( 4,0 ) , ( - 4,0 )(4,0),(−4,0)

Write an Equation for the Hyperbola $( 4,0 ) , ( - 4,0 )$