How do you convert #y= 3x^2-5x-y^2 # into a polar equation?

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Answer 1 · 2018-03-20T14:22:22

#r=-(sintheta+5costheta)/(sin^2theta-3cos^2theta)#

For this we need the following:
#x=rcostheta#
#y=rsintheta#

#rsintheta=3(rcostheta)^2-5(rcostheta)-(rsintheta)^2#

#rsintheta=3r^2cos^2theta-5rcostheta-r^2sin^2theta#

#rsintheta+r^2sin^2theta=3r^2cos^2theta-5rcostheta#

#sintheta+rsin^2theta=3rcos^2theta-5costheta#

#rsin^2theta-3rcos^2theta=-sintheta-5costheta#

#r=(-sintheta-5costheta)/(sin^2theta-3cos^2theta)=-(sintheta+5costheta)/(sin^2theta-3cos^2theta)#