by: Doris Santarone

**Assignment #11: Polar Equations**

In this assignment, I will investigate the effects of varying a, b, c, and k on several Polar Equations.

1)

__VARYING a__: I will set k = 0.1 and vary a. I will use a = 1, 2, 3, 5, and 10.

It looks like a affects the size of the "loop". See the movie below to watch how the graph changes as a varies from 0 to 10.

__VARYING k__: I will set a = 3 and vary k. I will use k = 1, 2, 3, 4, and 5.

k indicates the number of "loops" on the graph. See the movie below to watch how the graph changes as k varies from 0 to 10.

2)

__VARYING a__: I will set k = 0.1 and vary a. I will use a = 1, 2, 3, 5, and 10.

Again, you can see that a affects the size of the "loop." See the movie below to watch how the graph changes as a varies from 0 to 10.

__VARYING k__: I will set a = 3 and vary k. I will use k = 1, 2, 3, 4, and 5.

Again, k indicates the number of loops on the graph. View the movie below to see how the graph changes as k varies from 0 to 10.