Chapter 11.6, Problem 13E

To determine

To draw: the graph of the polar equations.

Explanation of Solution

Given information:

The polar equation is $r=\frac{3}{1-2\sin \theta }$ .

Graph: first write the equation in the standard equation,

  $r=\frac{2\left(\frac{3}{2}\right)}{1-2\sin \theta }$

since, the polar equation of conic is $r=\frac{2\left(\frac{3}{2}\right)}{1-2\sin \theta }$ , so the $e=2\text{ and }d=\frac{3}{2}$ ,

Thus, the conic is hyperbola which directrix is $y=-\frac{3}{2}$ .

Now, by using plotting point method,

$\theta$	$r$
$0$	$3$
$\pi$	$3$
$\frac{\pi }{2}$	$-3$

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 hyperbola.