Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$
A) $r= \frac { 7 } { 10 - 3 \sin \theta }$

B) $r= \frac { 2 } { 1 - 3 \sin \theta }$

C) $r= \frac { 21 } { 10 + 3 \sin \theta }$

D) $r = \frac { 21 } { 10 - 3 \sin \theta }$

E) $r= \frac { 21 } { 10 - 3 \cos \theta }$

Question

Write a polar equation of an ellipse with eccentricity $0.3$ and directrix $y = - 7$
A) $r= \frac { 7 } { 10 - 3 \sin \theta }$

B) $r= \frac { 2 } { 1 - 3 \sin \theta }$

C) $r= \frac { 21 } { 10 + 3 \sin \theta }$

D) $r = \frac { 21 } { 10 - 3 \sin \theta }$

E) $r= \frac { 21 } { 10 - 3 \cos \theta }$

Quizplus · Accepted Answer

The polar equation of an ellipse with eccentricity $e$ and directrix $y=k$ is given by $\gamma=\frac{r}{1-e^2}-k\cos{	heta}$.

Here, $e=0.3$ and $k=-7$. Thus, the polar equation of the ellipse is $\gamma=\frac{r}{1-0.3^2}-(-7)\cos{	heta}=\frac{21}{10-3\sin{	heta}}$. Therefore, the correct choice is D.

Write a Polar Equation of an Ellipse with Eccentricity 0.30.30.3 And Directrix

Write a Polar Equation of an Ellipse with Eccentricity $0.3$ And Directrix