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 = 2, x = -8
A) $r = \frac { 16 } { 1 - 2 \cos \theta }$
B) $r = \frac { 16 } { 1 + 2 \cos \theta }$
C) $r = \frac { 16 } { 1 + 8 \cos \theta }$
D) $r = \frac { 16 } { 1 - 2 \sin \theta }$

Question

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 = 2, x = -8 
A) $r = \frac { 16 } { 1 - 2 \cos \theta }$
B) $r = \frac { 16 } { 1 + 2 \cos \theta }$
C) $r = \frac { 16 } { 1 + 8 \cos \theta }$
D) $r = \frac { 16 } { 1 - 2 \sin \theta }$

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, $e = 2$ and $d = 8$, so the equation is $r = \frac{16}{1 - 2 \cos \theta}$.

The Eccentricity Is Given of a Conic Section with One r=161−2cos⁡θr = \frac { 16 } { 1 - 2 \cos \theta }r=1−2cosθ16​

The Eccentricity Is Given of a Conic Section with One $r = \frac { 16 } { 1 - 2 \cos \theta }$