Write a polar equation in r and $\theta$ of an ellipse with the focus at the origin, with the eccentricity $\frac { 2 } { 7 }$ and directrix $x = - 11$ .
A) $r = \frac { 11 } { 7 + 2 \cos \theta }$
B) $r = \frac { 22 } { 7 + 2 \cos \theta }$
C) $r = \frac { 22 } { 7 - 2 \cos \theta }$
D) $r = \frac { 2 } { 3 - 2 \sin \theta }$
E) $r = \frac { 22 } { 1 - 2 \cos \theta }$

Question

Quizplus · Accepted Answer

Since the focus is at the origin and the directrix is a vertical line, we know that the equation will be of the form $r = \frac{d}{1-e\cos	heta}$, where $d$ is the distance from the origin to the directrix and $e$ is the eccentricity. In this case, $d = 11$ and $e = \frac{2}{7}$, so we have:

$$r = \frac{11}{1 - \frac{2}{7}\cos	heta} = \frac{11}{\frac{5}{7} - \frac{2}{7}\cos	heta} = \frac{22}{10 - 4\cos	heta} = \frac{22}{7 - 2\cos	heta}$$

Therefore, the answer is (C).

Write a Polar Equation in R 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