Let \mathcal{E} be an ellipse with foci F_{1} and F_{2}. Parabola \mathcal{P}, having vertex F_{1} and focus F_{2}, intersects \mathcal{E} at two points X and Y. Suppose the tangents to \mathcal{E} at X and Y intersect on the directrix of \mathcal{P}. Compute the eccentricity of \mathcal{E}.
(A parabola \mathcal{P} is the set of points which are equidistant from a point, called the focus of \mathcal{P}, and a line, called the directrix of \mathcal{P}. An ellipse \mathcal{E} is the set of points P such that the sum P F_{1}+P F_{2} is some constant d, where F_{1} and F_{2} are the foci of \mathcal{E}. The eccentricity of \mathcal{E} is defined to be the ratio F_{1} F_{2} / d.)