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

1 Answer
Mar 20, 2018

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

Explanation:

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)#