Find a Polar Equation of the Conic with Focus at the Pole

Multiple Choice

Find a polar equation of the conic with focus at the pole that has the eccentricity and equation of directrix. $e = 4 , \quad r = - 2 \csc \theta$

A) $r = \frac { 8 } { 1 - 4 \sin \theta }$
B) $r = \frac { 8 } { 2 + \sin \theta }$
C) $r = \frac { 8 } { 1 - 4 \cos \theta }$
D) $r = \frac { 2 } { 4 + \cos \theta }$
E) $r = \frac { 8 } { 1 + 4 \sin \theta }$