Remember that transformation between Cartesian and polar system are:
x=rcos(α)
y=rsin(α)
From this we can conclude that:
r=√(x^2 + y^2)
Using trigonometry transformations we can write:
r=sin(2α) = 2sin(α)cos(α)
Now we can multiply both sides with r^2:
r^3 = 2(rsin(α))(rcos(α))
Now using some replacements we can write:
(x^2 + y^2)^(3/2) = 2x*y
