Chapter 11.6, Problem 14E

To determine

To draw: the graph of the polar equations.

Explanation of Solution

Given information:

The polar equation is $r=\frac{5}{3-3\sin \theta }$ .

Graph: first write the equation in the standard equation,

  $r=\frac{1\left(\frac{5}{3}\right)}{1-\sin \theta }$

since, the polar equation of conic is $r=\frac{1\left(\frac{5}{3}\right)}{1-\sin \theta }$ , so the $e=1\text{ and }d=\frac{5}{3}$ ,

Thus, the conic is parabola which directrix is $y=-\frac{5}{3}$ .

Now, by using plotting point method,

$\theta$	$r$
$0$	$\frac{5}{3}$
$\pi$	$\frac{5}{3}$
$\frac{\pi }{6}$	$\frac{10}{3}$

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 parabola.