Well I've figured out how to do most of my questions I need to get done, but there are still a few that I cannot quite figure out.

r = 1 + 18cosѲ

r^2 = r + 8rcosѲ

x^2 + y^1 = r + 8y

This is where I get stumped.

8x^2 + 8y^2 - 88y = 0

x^2 + Y^2 - 11y = 0

r^2 - 11cosѲ = 0

r(r - 11cosѲ) = 0

r=11cosѲ

Not sure if I did this one correctly.