The conversion to polar from Cartesian is x=rcosø and y=rsinø, and r^2=x^2+y^2.
Rewriting the equation: (x^2+y^2)^3=4x^2y^2 we have r^6=4r^4sin^2(ø)cos^2(ø). In general, we can write r^2=4sin^(ø)cos^2(ø) or r=2sinøcosø=sin(2ø) (strictly r=±sin(2ø)).
At ø=0, r=0; when ø=π/4 r=1 (maximum absolute length); ø=π/2, r=0. Other values: ø=π/12, r=0.5; ø=π/6,r=√3/2; ø=π/8, r=√2/2; ø=π/3, r=√3/2. The pattern is one consisting of 4 symmetrical leaves joined at the origin as r increases from zero to length 1 as ø goes from zero to π/4. Between π/4 and π/2 r decreases from 1 back to zero. The central axes of the leaves cross at right angles like a tilted + sign and the angle of tilt is 45 degrees.