Find a Polar Equation for the Conic Described $\left( 4 , \frac { \pi } { 2 } \right)$

Multiple Choice

Find a polar equation for the conic described.
-The hyperbola with a focus at the pole and transverse axis endpoints $\left( 4 , \frac { \pi } { 2 } \right)$ and $\left( - 8 , \frac { 3 \pi } { 2 } \right)$

A) $r = \frac { 16 } { 1 + 3 \sin \theta }$
B) $r = \frac { 16 } { 1 - 3 \sin \theta }$
C) $r = \frac { 8 } { 2 + 6 \sin \theta }$
D) $r = \frac { 16 } { 1 + 3 \cos \theta }$