How do you convert #2y= -3x^2+9x # into a polar equation?

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Answer 1 · 2017-09-19T09:17:59

#r=3sectheta-2/3secthetatantheta#

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

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

Hence, #2y=-3x^2+9x# can be written as

#2rsintheta=-3r^2cos^2theta+9rcostheta#

or #2sintheta=-3rcos^2theta+9costheta#

or #3rcos^2theta=9costheta-2sintheta#

or #r=(9costheta)/(3cos^2theta)-(2sintheta)/(3cos^2theta)#

or #r=3sectheta-2/3secthetatantheta#