$Y=mx$ is a chord of circle of radius $a$ through the origin whose diameter is along the $x$-axis. Find the equation of the circle whose diameter is the chord.
We also need to find the locus of its centre. I got a relation $h=m^2 h+(a^2+c)^.5$. Where $h$ is abscissa of the centre, $c$ is the constant term in the circle's equation.