A circle with the vertex of parabola $C$ as its center intersects $C$ at points $A , B$, and intersects the directrix of $C$ at points $D , E$. If $|DE| = 2 \sqrt { 5 }$, then the distance from the focus of $C$ to the directrix is
(A) 2
(B) 4
(C) 6
(D) 8