Chapter 11.6, Problem 12E

To determine

To draw: the graph of the polar equations.

Explanation of Solution

Given information:

The polar equation is $r=\frac{2}{2-\cos \theta }$ .

Graph: first write the equation in the standard equation,

  $r=\frac{\frac{1}{2}\left(2\right)}{1-\frac{1}{2}\cos \theta }$

since, the polar equation of conic is $r=\frac{\frac{1}{2}\left(2\right)}{1-\frac{1}{2}\cos \theta }$ , so the $e=\frac{1}{2}\text{ and }d=2$ ,

Thus, the conic is ellipse which directrix is $x=-2$ .

Now, by using plotting point method,

$\theta$	$r$
$0$	$2$
$\frac{\pi }{2}$	$1$
$2\pi$	$2$

Now, using the above table and join the points,

The graph can be obtained as:

  

Interpretation: from the above graph it can be observed that for the polar equation the conic is ellipse.