Consider the parabola P: y^2=4 k x and the ellipse E: x^2/a^2+y^2/b^2=1. Let the line segment joining the points of intersection of P and E, be their…

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