How do you convert #y= 3x^2 -2xy+4xy^2 # into a polar equation?

1 Answer
Shwetank Mauria
Nov 8, 2016

#4r^2costhetasin^2theta+r(3cos^2theta-2costhetasintheta)-sintheta=0#

Explanation:

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

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

Hence, #y=3x^2-2xy+4xy^2#

#hArrrsintheta=3r^2cos^2theta-2r^2costhetasintheta+4r^3costhetasin^2theta#

or #sintheta=3rcos^2theta-2rcosthetasintheta+4r^2costhetasin^2theta#

#4r^2costhetasin^2theta+r(3cos^2theta-2costhetasintheta)-sintheta=0#

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