JEE Main 2025 — Ellipse Question with Solution

The centre of a circle C is at the centre of the ellipse $\mathrm{E}:\frac{x^2}{{\mathrm{a}}^2}+\frac{y^2}{{\mathrm{b}}^2}=1,\mathrm{a}>\mathrm{b}$. Let C pass through the foci $F_1$ and $F_2$ 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 ${\mathrm{PF}}_1{\mathrm{F}}_2$ is 30 and the length of the major axis of $E$ is 17 , then the distance between the foci of $E$ is :