by Courrey J. Alexander

This assignment is an investigation of the
polar equation of the form r=a+b cos (kθ).

First, letŐs examine the graph of a = b for
k=5.

To see what happens when a=b as k varies from
-10 to 10, ** click here**.

Below is a picture where k=1, 2, and 3 for
a=b.

What happens if we vary *a* , keeping *b*
and *k* constant? Below is a graph
for k=1 and b=5 for different values of a. Click on the graph to see its behavior as a varies from -10
to 10.

Below is a graph for the same values of a
when k=3.

Now let's look at what happens when we vary b
while a and k remain constant. Below is a graph for different values of b when
a=3 and k=1.

Below is another graph for the same values of
b when k=2.