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

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Answer 1 · 2017-06-04T20:20:11

The polar equation is #r=(sintheta+4costheta)/(sin^2theta-2cos^2theta)#

To convert from rectangular coordinates #(x,y)# to polar coordinates #(r,theta)#, we use the following

#x=rcostheta#

#y=rsintheta#

Our equation is

#y=y^2-2x^2-4x#

#rsintheta=r^2sin^2theta-2r^2cos^2theta-4rcostheta#

Dividing by #r!=0#

#sintheta=rsin^2theta-2rcos^2theta-4costheta#

#r(sin^2theta-2cos^2theta)=sin theta+4costheta#

#r=(sintheta+4costheta)/(sin^2theta-2cos^2theta)#