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

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Answer 1 · 2016-05-19T10:43:15

Polar equation is #r=(sintheta-3costheta)/(cos^2theta+2cos2theta)#

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

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

Using them we can convert #y=3x^2+3x-2y^2# as follows.

#y=3x^2+3x-2y^2#

or #rsintheta=3(rcostheta)^2+3rcostheta-2(rsintheta)^2#

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

or #rsintheta=r^2cos^2theta+3rcostheta+2r^2(cos^2theta-sin^2theta)#

or #sintheta=rcos^2theta+3costheta+2rcos2theta#

or #r=(sintheta-3costheta)/(cos^2theta+2cos2theta)#