Converting Polar Equation to Rectangular Form?

Question

How do you convert r^2=sin2theta to rectangular form? Any help is greatly appreciated!!!

Answer 1

r² = sin2θ

.....= 2sinθcosθ

..... = 2.y/r. x/r

..... = 2xy/r²

(r²)² = 2xy

(x² + y²)² = 2xy

Answer 2

r^2 = x^2 + y^2
sin 2θ = 2 sin θ cos θ
= (2/r^2) (r sin θ . r cos θ)
= (2 / (x+2 + y^2)) (y.x)
So we get
x^2 + y^2 = 2xy / (x^2 + y^2)
or
(x^2 + y^2)^2 = 2xy.