Coordinate Geometry: JEE Main 2026 Mathematics question

Consider the parabola $P: y^2=4kx$ and the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. Let the line segment joining the points of intersection of P and E, be their latus rectums. If the eccentricity of E is $e$, then $e^2+2\sqrt2$ is equal to ______.