This assignment is an investigation of the polar equation of the form .

Let's look at what happens when we keep a=b. A graph when a = b for k=7 would look like the following:

For a a graphing calculator picture of what happens for a=b as k varies, click here.

Below is a picture where k=1 (purple), k=2 (red), and k=3(blue) for a=b.

What happens if we vary a and hold b and k constant? Below is a graph for k=1 and b=5 for different values of a.

Purple: a=1, Red: a=2, Blue: a=3, and Green a=4.

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

Now let's look at what happens when we vary b and leave a and k constant. Below is a graph for different values of b when a=3 and k=1. Purple: b=1, Red: b=2, Blue: b=3, Green: b=4, Light blue: b=5.

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

To see a graphing calculator picture for the graph for different values of b when k=4, click here.