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.
$\begin{array} { l c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \\ \text { Ellipse } & e = \frac { 1 } { 2 } & y = 5 \end{array}$

A) $r = \frac { 1 } { 2 + \cos \theta }$
B) $r = \frac { 5 } { 2 + \cos \theta }$
C) $r = \frac { 5 } { 2 - \cos \theta }$
D) $r = \frac { 5 } { 2 - \sin \theta }$
E) $r = \frac { 5 } { 2 + \sin \theta }$