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 $\frac { 7 } { 2 }$ , and directrix $y = - 7$ . Identify the conic.

A)
$r = \frac { 49 } { 2 - 7 \cos \theta }$ , hyperbola
B)
$r = \frac { 49 } { 2 - 7 \sin \theta }$ , hyperbola
C) $r = \frac { 49 } { 2 - \sin \theta }$ , ellipse
D) $r = \frac { 49 } { 2 - \cos \theta }$ , ellipse