Question

Find the coordinates of the centres and the radii of the circles whose equation is:
$x^2+y^2=k(x+k)$

Answer 1

Given circle can be written as, $x^2+y^2-kx-k^2=0$

Now comparing with general equation of circle, $x^2+y^2+2gx+2fy+c=0$

we get centre of the circle $=(-g,-f)=(\frac{k}{2},0)$

and radius $=\sqrt{g^2+f^2-c}=\sqrt{\frac{k^2}{4}+k^2}=\frac{\sqrt{5}}{2}k$