Problem 63E
Tracing hyperbolas and parabolas Graph the following equations. Then use arrows and labeled points to indicate how the curve is generated as θ increases from 0 to 2π.
Solution 63E
Step 1:
In this problem we have to draw the graph of r = and then use arrows and labeled points to indicate how the curve is generated as increases from 0 to 2.
We know that the polar equation of parabola , with focus at origin , and opening along positive xaxis.
r = , where a = distance from focus to vertex.
The graph of r = is shown below:
r = 

r = = 
0 
r = = 3 

r = = 

r = = 3 

r = =

2 
As increases from 0 to 2 , the curve generated as a circle , and at = 0 and 2 the curve approaches to infinity.