How do you convert #2y= 7x^2-2x # into a polar equation?

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Answer 1 · 2016-12-01T17:16:08

#r=(2(sintheta+costheta))/(7cos^2theta)#

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

#x=rcostheta# and #y=rsintheta#

Hence #2y=7x^2-2x# van be written as

#2rsintheta=7(rcostheta)^2-2rcostheta#

or #2rsintheta+2rcostheta=7r^2cos^2theta#

or #2r(sintheta+costheta)=7r^2cos^2theta#

or #r=(2(sintheta+costheta))/(7cos^2theta)#