convert the equation to polar coordinates and simplify. (x^2+y^2)^2=2xy

Answer 1

x²+y²=r²

x=rcos(θ)

y=rsin(θ)

knowing this let's plug in

r⁴=2(rcos(θ))(rsin(θ)), r⁴=2r²cos(θ)sin(θ), r²=2cos(θ)sin(θ), r²=sin(2θ)