How do you convert #y= 3x^2 -2x-xy^2 # into a polar equation?

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Answer 1 · 2017-03-10T16:15:53

#r^2sin^2theta-3rcostheta+tantheta+2=0#

The relation between rectangular coordinates #(x,y)# and polar coordinates #(r,theta)# is given by

#x=rcostheta#, #y=rsintheta#, #r^2=x^2+y^2#

Hence #y=3x^2-2x-xy^2# can be written as

#rsintheta=3r^2cos^2theta-2rcostheta-r^3costhetasin^2theta#

or #sintheta=3rcos^2theta-2costheta-r^2costhetasin^2theta#

or #r^2costhetasin^2theta-3rcos^2theta+sintheta+2costheta=0#

or #r^2sin^2theta-3rcostheta+tantheta+2=0#