Convert (x-1)^2 +y^2=1 to a polar equation

Answer 1

just crank it out.
(rcosθ - 1)^2 + r^2 sin^2θ = 1
r^2 cos^2θ - 2rcosθ + r^2 sin^2θ = 1
r^2 - 2rcosθ - 1 = 0

see the graph, which is, as expected, a circle with center at (1,0)

https://www.wolframalpha.com/input/?i=r%5E2+-+2rcos%CE%B8+-+1+%3D+0