2011 AMC 12B Problem 14

A segment through the focus F of a parabola with vertex V is perpendicular to \overline{FV} and intersects the parabola in points A and B. What is \cos\left(\angle AVB\right)?

\textbf{(A)}\ -\frac{3\sqrt{5}}{7} \qquad \textbf{(B)}\ -\frac{2\sqrt{5}}{5} \qquad \textbf{(C)}\ -\frac{4}{5} \qquad \textbf{(D)}\ -\frac{3}{5} \qquad \textbf{(E)}\ -\frac{1}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.