Find a polar equation for the conic. A focus is at the pole.
-$e = 5$; directrix is perpendicular to the polar axis 3 to the right of the pole
A) $r = \frac { 15 } { 1 + 5 \cos \theta }$
B) $r = \frac { 15 } { 1 + 5 \sin \theta }$
C) $r = \frac { 15 } { 1 - 5 \sin \theta }$
D) $r = \frac { 15 } { 1 - 5 \cos \theta }$

Question

Quizplus · Accepted Answer

The polar equation for a conic with a focus at the pole is $r = \frac { ed } { 1 \pm e \cos \theta }$ or $r = \frac { ed } { 1 \pm e \sin \theta }$, where $e$ is the eccentricity and $d$ is the distance to the directrix. Since the directrix is perpendicular to the polar axis and 3 units to the right of the pole, we use the cosine form. The directrix being 3 units away and $e = 5$, the equation becomes $r = \frac { 15 } { 1 + 5 \cos \theta }$.

Find a Polar Equation for the Conic e=5e = 5e=5 ; Directrix Is Perpendicular to the Polar Axis 3 to at the Pole

Find a Polar Equation for the Conic $e = 5$ ; Directrix Is Perpendicular to the Polar Axis 3 to at the Pole