The centre of a circle C is at the centre of the ellipse E: x^2/(a^2)+y^2/(b^2)=1, a > b. Let C pass through the foci F_1 and F_2 of E such that the…

The centre of a circle C is at the centre of the ellipse $\displaystyle \mathrm{E}: \frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}=1, \mathrm{a}>\mathrm{b}$. Let C pass through the foci $\displaystyle \mathrm{F}_1$ and $\displaystyle \mathrm{F}_2$ of E such that the circle C and the ellipse E intersect at four points. Let P be one of these four points. If the area of the triangle $\displaystyle \mathrm{PF}_1 \mathrm{~F}_2$ is $\displaystyle 30$ and the length of the major axis of E is $\displaystyle 17$, then the distance between the foci of E is :