An ellipse having foci at  $(3, 3) and (-4, 4)$and passing through the origin, then the eccentricity of the ellipse is

The ellipse is passing through O(0, 0) and has foci $\mathrm{P}(3,3)\text{ and }\mathrm{Q}(-4,4)$ then 
$\begin{array}{l}\mathrm{OP}+\mathrm{OQ}=2\mathrm{a}\text{ and }\mathrm{PQ}=2\mathrm{ae}\\ \therefore \mathrm{e}=\frac{\mathrm{PQ}}{\mathrm{OP}+\mathrm{OQ}}=\frac{\sqrt{50}}{3\sqrt{2}+4\sqrt{2}}=\frac{5}{7}\end{array}$