Find a Polar Equation of the Conic with the Given $\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \\ \text { Parabola } & e = 1 & x = - 4 \end{array}$

Multiple Choice

Find a polar equation of the conic with the given characteristics and with one focus at the pole. $\begin{array} { c c c } \text { Conic } & \text { Eccentricity } & \text { Directrix } \\ \text { Parabola } & e = 1 & x = - 4 \end{array}$

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