Solve the Problem $44 \mathrm {~cm}$ Apart the Distance of the Vertex from One Focus Is

Multiple Choice

Solve the problem.
-For a hyperbolic mirror the two foci are $44 \mathrm {~cm}$ apart. The distance of the vertex from one focus is 10 $\mathrm { cm }$ and from the other focus is $34 \mathrm {~cm}$ . 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) $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 340 } = 1$
B) $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 340 } = 1$
C) $\frac { y ^ { 2 } } { 144 } - \frac { x ^ { 2 } } { 340 } = 5$
D) $\frac { x ^ { 2 } } { 144 } - \frac { y ^ { 2 } } { 340 } = 5$