Suppose \mathcal{E}_{1} \neq \mathcal{E}_{2} are two intersecting ellipses with a common focus X; let the common external tangents of \mathcal{E}_{1} and \mathcal{E}_{2} intersect at a point Y. Further suppose that X_{1} and X_{2} are the other foci of \mathcal{E}_{1} and \mathcal{E}_{2}, respectively, such that X_{1} \in \mathcal{E}_{2} and X_{2} \in \mathcal{E}_{1}. If X_{1} X_{2}=8, X X_{2}=7, and X X_{1}=9, what is X Y^{2}?