Find a Polar Equation of the Conic with the Given

Multiple Choice

Find a polar equation of the conic with the given characteristics and with one focus at the pole.
$\begin{array} { l l } \text { Conic } & \text { Vertices } \\ \text { Hyperbola } & \left( \frac { 2 } { 3 } , \frac { \pi } { 2 } \right) , \left( - 2 , \frac { 3 \pi } { 2 } \right) \end{array}$

A) $r = \frac { 2 } { 1 - 2 \sin \theta }$
B) $r = \frac { 2 } { 1 + 2 \sin \theta }$
C) $r = \frac { 2 } { 1 + 2 \cos \theta }$
D) $r = \frac { 2 } { 1 - 2 \cos \theta }$
E) $r = \frac { 2 } { 1 + 1 \cos \theta }$