Find a Polar Equation for the Conic $\mathrm { e } = \frac { 1 } { 2 } ;$

Multiple Choice

Find a polar equation for the conic. A focus is at the pole.
- $\mathrm { e } = \frac { 1 } { 2 } ;$ directrix is perpendicular to the polar axis 2 to the left of the pole

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