How do you find the polar equation for #3x^2+3y^2-2x=0#?

Question

6071 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-03T07:08:28

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#

Answer 2 · 2016-12-03T07:08:34

#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#