Find an equation of the hyperbola centered at the origin that satisfies the given condition.
Vertices: $( \pm 4,0 )$, asymptotes: $y = \pm \frac { 7 } { 4 } x$
A) $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 49 } = 1$
B) $\frac { y ^ { 2 } } { 49 } - \frac { x ^ { 2 } } { 16 } = 1$
C)
$\frac { y ^ { 2 } } { 16 } - \frac { x ^ { 2 } } { 49 } = 1$
D)
$\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 16 } = 1$

Question

Quizplus · Accepted Answer

The transverse axis is horizontal, so the equation has the form $\frac { x ^ { 2 } } { b ^ { 2 } } - \frac { y ^ { 2 } } { a ^ { 2 } } = 1$. The vertices are $(\pm 4,0)$, so $b=4$. The asymptotes have slopes $\pm \frac { a } { b } = \pm \frac { 7 } { 4 }$, so $a=7$. Therefore, the equation is $\frac { x ^ { 2 } } { 16 } - \frac { y ^ { 2 } } { 49 } = 1$.

Find an Equation of the Hyperbola Centered at the Origin (±4,0)( \pm 4,0 )(±4,0)

Find an Equation of the Hyperbola Centered at the Origin $( \pm 4,0 )$