Find a polar equation for the ellipse with its focus at the pole, eccentricity , and directrix .

Question

Find a polar equation for the ellipse with its focus at the pole, eccentricity  , and directrix  .

Quizplus · Accepted Answer

Since the focus is at the pole, we know that the polar equation will have the form $r = \frac{ed}{1-e\cos	heta}$, where $e$ is the eccentricity and $d$ is the distance from the pole to the directrix. Plugging in the given values, we get $r=\frac{11}{1-\frac{1}{11}\cos	heta}$ or $r=\frac{11}{\frac{10}{11}-\cos	heta}$. This can be simplified by multiplying the top and bottom by the conjugate of the denominator, which gives $r=\frac{11(\frac{10}{11} + \cos 	heta)}{1- \cos^2	heta} = \boxed{11eaa595\_6417\_c185\_a696\_e901b5f8a231\_TB4584\_11\_TB4584\_11}$.

Find a Polar Equation for the Ellipse with Its Focus