What is the polar form of the equation: x^2+y^2 =xy+1

Using Pythagoras, x² + y² = r².Using basic trigonometry, x = rsinθ and y = rcosθ.
xy + 1 = r²sinθcosθ + 1 = (1/2)r²sin2θ + 1
Subbing in both halves and doubling gives:2r² = r²sin2θ + 2
-> r²(2 - sin2θ)r² = 2
-> r² = 2/(2-sin2θ)