Problem 64E
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 64E
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 a hyperbola having center at a focus is ; r =
The graph of r = is shown below ;
r = 

r = = 1 
0 
r = = 1 

r = = 

r = = 1 

r = =

2 
As increases from 0 to 2 , the curve generated as a circle.