Concyclic Points on a Parabola

Let $0 < a < b$. Lines $\ell$ and $m$ pass through $A(a, 0)$ and $B(b, 0)$ respectively, and meet the parabola $y^2 = x$ in four distinct points. When those four points are concyclic, find the locus of the intersection $P$ of $\ell$ and $m$.