Write a Polar Equation of the Conic That Has a Focus

Multiple Choice

Write a polar equation of the conic that has a focus at the origin, eccentricity $\frac { 3 } { 2 }$ , and directrix $x = - 6$ . Identify the conic.

A) $r = \frac { 18 } { 2 - 3 \sin \theta }$ , hyperbola
B) $r = \frac { 18 } { 2 - 3 \cos \theta }$ , hyperbola
C) $r = \frac { 18 } { 2 - \cos \theta }$ , ellipse
D) $r = \frac { 18 } { 2 - \sin \theta }$ , ellipse