Write a Polar Equation in R And $\theta$ Of a Hyperbola with the Focus at the Origin, with Hyperbola

Multiple Choice

Write a polar equation in r and $\theta$ of a hyperbola with the focus at the origin, with the eccentricity $5$ and directrix $r = - 10 \csc \theta$ .

A) $r = \frac { 50 } { 1 - 5 \sin \theta }$
B) $r = \frac { 50 } { 1 - 50 \sin \theta }$
C) $r = \frac { 50 } { 1 - \sin \theta }$
D) $r = \frac { 10 } { 1 + 10 \sin \theta }$
E) $r = \frac { 50 } { 1 + 5 \sin \theta }$