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

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Answer 1 · 2017-05-24T16:59:56

#r^2sintheta(costheta+3sintheta)-rcostheta+2=0#

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

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

Hence we can write #xy=x-2-3y^2# in polar form as

#rcosthetaxxrsintheta=rcostheta-2-3r^2sin^2theta#

or #r^2sinthetacostheta=rcostheta-2-3r^2sin^2theta#

or #r^2(sinthetacostheta+3sin^2theta)-rcostheta+2=0#

or #r^2sintheta(costheta+3sintheta)-rcostheta+2=0#