Write a Polar Equation In $\mathrm { r }$ And $\theta$ Of a Hyperbola with the Focus at the Origin, with \theta

Multiple Choice

Write a polar equation in $\mathrm { r }$ and $\theta$ of a hyperbola with the focus at the origin, with the eccentricity 7 and directrix $r = - 12 \csc \theta$ .

A) $r = \frac { 84 } { 1 - 84 \sin \theta }$
B) $r = \frac { 84 } { 1 - 7 \sin \theta }$
C) $r = \frac { 84 } { 1 + 7 \sin \theta }$
D) $r = \frac { 84 } { 1 - \sin \theta }$
E) $r = \frac { 12 } { 1 + 12 \sin \theta }$