Convert cartesian equation to polar form

Question

1. x^2+y^2=4x

2. (x^2+y^2)^2=6(x^2-y^2)

Answer 1

These take some practice, but you soon learn the tricks of thinking...

#1
r^2 = 4r cosθ
r = 4cosθ

#2
(r^2)^2 = 6(r^2 cos^2θ - r^2 sin^2θ)
r^2 = 6(cos^2θ - sin^2θ)
r^2 = 6cos(2θ)