Chapter 11.6, Problem 8E

To determine

To find: the polar equation of conic.

Answer to Problem 8E

The polar equation of conic is $r=\frac{6}{5+3\sin \theta }$ .

Explanation of Solution

Given information:

ellipse, Focus: $\left(0,0\right)$ , eccentricity $0.6$ , directrix $r=2\csc \theta$ .

Calculation: since, the directrix of the ellipse is $r=2\csc \theta$ , so the standard polar equation is,

  $r=\frac{ed}{1+e\sin \theta }$

Since, directrix is $r=2\csc \theta$ , so $d=2$

Now, substitute in the standard polar equation and then simplify,

  $\begin{array}{l}r=\frac{ed}{1+e\sin \theta }\\ r=\frac{\left(0.6\right)2}{1+\left(0.6\right)\sin \theta }\text{ [substitute]}\\ r=\frac{6}{5+3\sin \theta }\text{ [simplify]}\end{array}$

Thus, the polar equation of ellipse is $r=\frac{6}{5+3\sin \theta }$ .