Write a Polar Equation of a Hyperbola with Eccentricity $3$ And Directrix

Multiple Choice

Write a polar equation of a hyperbola with eccentricity $3$ and directrix $r = 2 \csc \theta$

A) $r= \frac { 3 } { 1 + 3 \cos \theta }$

B) $r = \frac { 3 } { 1 - 3 \sin \theta }$

C) $r = \frac { 2 } { 2 + 3 \cos }$

D) $r = \frac { 6 } { 1 + 3 \sin \theta }$

E) $r= \frac { 6 } { 1 - 3 \sin \theta }$