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.