The eccentricity is given of a conic section with one focus at the origin, along with the directrix corresponding to that focus. Find a polar equation for the conic section.
-$$e = \frac { 1 } { 4 } , x = 2$$
A) $r = \frac { 2 } { 4 + \cos \theta }$
B) $r = \frac { 2 } { 4 + \sin \theta }$
C) $r = \frac { 2 } { 1 + 4 \cos \theta }$
D) $r = \frac { 2 } { 4 - \cos \theta }$

Question

Quizplus · Accepted Answer

The polar equation of a conic section with eccentricity $e$ and directrix $x = d$ is $r = \frac{ed}{1 + e \cos \theta}$. Here, $e = \frac{1}{4}$ and $d = 2$, so the equation is $r = \frac{2}{4 + \cos \theta}$.

The Eccentricity Is Given of a Conic Section with One e=14,x=2e = \frac { 1 } { 4 } , x = 2e=41​,x=2

The Eccentricity Is Given of a Conic Section with One $e = \frac { 1 } { 4 } , x = 2$