Question

Find the center and radius of the circle whose equation is given by: $2x^2+2y^2-x=0$

Answer 1

$2x^2+2y^2-x=0$

$x^2+y^2-\frac{x}{2}=0$

We have the general for the equation of the circle $x^2+y^2+2gx+2fy+c=0$

The center of the circle is given by $(-g,-f)$

Here,

$f=0$

$2g=-\frac{1}{2}$

$⟹g=-\frac{1}{4}$

$\therefore center=(-g,-f)=(\frac{1}{4},0)$

$radius=\sqrt{g^2+f^2-c}=\sqrt{\frac{1}{4}}=\frac{1}{2}$