The equation is #3r-2costheta=0#
To convert from cartesian coordinates #(x,y)# to polar coordinates #(r, theta)# , we use the following
#x=rcostheta#
#y=rsintheta#
#x2+y^2=r^2#
Our equation is
#3x^2+3y^2-2x=0#
#3(x^2+y^2)-2x=0#
So,
#3r^2-2rcostheta=0#
#r(3r-2costheta)=0#
#3r-2costheta=0#
The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is given by
#x=rcostheta# and #y=rsintheta# i.e. #tantheta=y/x# and #r^2=x^2+y^2#
Hence #3x^2+3y^2-2x=0hArr3(x^2+y^2)-2x=0#
or #3r^2-2rcostheta=0#
or #3r-2costheta=0#
How do you find the polar equation for #3x^2+3y^2-2x=0#?
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