Write a polar equation in $r$ and $\theta$ of an ellipse with the focus at the origin, with the eccentricity $\quad \frac { 6 } { 7 }$ and directrix $x = - 13$.
A) $r = \frac { 78 } { 7 - 6 \cos \theta }$
B) $r = \frac { 13 } { 7 + 6 \cos \theta }$
C) $r = \frac { 78 } { 1 - 6 \cos \theta }$
D) $r = \frac { 78 } { 7 + 6 \cos \theta }$
E) $r = \frac { 6 } { 3 - 6 \sin \theta }$

Question

Quizplus · Accepted Answer

The polar equation of an ellipse with a focus at the origin is given by $r = \frac { ed } { 1 - e \cos \theta }$, where $e$ is the eccentricity and $d$ is the distance to the directrix. Given $e = \frac { 6 } { 7 }$ and $d = 13$, the equation becomes $r = \frac { 78 } { 7 - 6 \cos \theta }$.

Write a Polar Equation In rrr And θ\thetaθ Of an Ellipse with the Focus at the Origin, with Ellipse

Write a Polar Equation In $r$ And $\theta$ Of an Ellipse with the Focus at the Origin, with Ellipse