Question

How do you convert rectangular equations into polar equations? If x4−y4=xy , then

r2=atan(b); What is a? What is b?

Answer 1

I would do it like this:
x^4 - y4 = xy
r^4(cos^4Ø) - r^4(sin^4Ø) = rcosØ(rsinØ)
divide by r^2, and factor the left part
r^2(cos^2Ø+sin^2Ø)(cos^2Ø - si^2Ø) = sinØcosØ
r^2(1)(cos 2Ø) = (1/2)sin 2Ø
r^2 = (1/2)tan(2Ø)

there is a polar equation