Write a polar equation in $r$ and $\theta$ of an ellipse with the focus at the origin, with the eccentricity $0.8$ and vertex at $\left( 1 , \frac { \pi } { 2 } \right)$.
A) $r = \frac { 1.8 } { 1 - 4 \cos \theta }$
B) $r = \frac { 9 } { 1 + 4 \sin \theta }$
C) $r = \frac { 1.8 } { 5 - 4 \cos \theta }$
D) $r = \frac { 9 } { 5 + 4 \sin \theta }$
E) $r = \frac { 9 } { 5 - 4 \cos \theta }$

Question

Quizplus · Accepted Answer

The polar equation of an ellipse with focus at the origin is $ r = \frac{ed}{1 + e \sin \theta} $ or $ r = \frac{ed}{1 + e \cos \theta} $. Given eccentricity $ e = 0.8 $ and vertex at $ \left( 1 , \frac{\pi}{2} \right) $, the equation is $ r = \frac{9}{5 + 4 \sin \theta} $ because the vertex is on the positive y-axis, indicating a sine function.

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