Let C(c, α) be the centre and 'a' be the radius of the circle.
Let P(r, θ) be a point on the circle.
∠XOC = α, OC = c
∠XOP = θ, OP = r, CP = a
∠COP = (θ – α)
By using cosine rule in ΔCOP,
(CP)2 = (OP)2 + (OC)2 – 2(OP)(OC) cos ∠COP
∴ a2 = r2 + c2 – 2rc cos(θ – α)
This is the required equation of circle.