The parabola $C : x ^ { 2 } = - 2 p y$ passes through the point $( 2 , - 1 )$.
(I) Find the equation of parabola $C$ and the equation of its directrix;
(II) Let $O$ be the origin. A line $l$ with non-zero slope passes through the focus of parabola $C$ and intersects parabola $C$ at two points $M , N$. The line $y = - 1$ intersects lines $O M$ and $O N$ at points $A$ and $B$ respectively. Prove that the circle with $A B$ as diameter passes through two fixed points on the $y$-axis.