r=1-rcos(theta)convert into rectangular equation?

Question

r with cos creating trouble for me how to solve this?

Answer 1

r = 1 - r cosθ
r(1+cosθ) = 1
r = 1/(1+cosθ)

You should recognize this as a parabola. Now for the conversion.

r = 1 - r cosθ
r^2 = (1 - r cosθ)^2
x^2+y^2 = 1 - 2x + x^2
y^2 = 1-2x