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

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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 $3r-2costheta=0$

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