For any tangent to $x^2$/$a^2$ + $y^2$/$b^2$ = 1, the product of perpendicular distances from the two foci to the tangent equals $b^2$. This is a classical result used in proving the reflection property and in optimization problems. The sum of squares of these distances is 2(a^{2-b}^2*$cos^2$(something)), but the product is simply $b^2$.