How do you convert #y=(x-y)^2-x^2y +xy^2 # into a polar equation?

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Answer 1 · 2016-04-15T21:49:30

#0=r^2-r^2sin(2theta)-1/2 r^3costhetasin(2theta)+1/2r^3sinthetasin(2theta)-rsintheta#

#0=x^2-2xy+y^2-x^2y+xy^2-y#

#0=x^2+y^2-2xy-x^2y+xy^2-y#

use formulas:
#x^2+y^2=r^2,x=rcostheta,y=rsintheta#

#0=r^2-2rcosthetaxxrsintheta-r^2cos^2thetaxxrsintheta+rcos thetaxxr^2sin^2theta-rsintheta#

#0=r^2-2r^2sinthetacostheta-r^3sinthetacos^2theta+r^3sin^2thetacostheta-rsintheta#

#0=r^2-r^2(2sinthetacostheta)-1/2 r^3costheta(2sinthetacostheta)+1/2r^3 sintheta(2sinthetacostheta)-rsintheta#

#0=r^2-r^2sin(2theta)-1/2 r^3costhetasin(2theta)+1/2r^3sinthetasin(2theta)-rsintheta#