Write an Equation for the Hyperbola $40 \mathrm {~cm}$ Apart the Distance of the Vertex from One Focus Is

Write an equation for the hyperbola.
-For a hyperbolic mirror the two foci are $40 \mathrm {~cm}$ apart. The distance of the vertex from one focus is 8 $\mathrm { cm }$ and from the other focus is $32 \mathrm {~cm}$ . Position a coordinate system with the origin at the center of the hyperbola and with the foci on the $y$ -axis. Find the equation of the hyperbola.

A) $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 1$

B) $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 256 } = 1$

C) $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 256 } = 5$

D) $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 256 } = 5$