Let P be a parabola with vertex (2,3) and directrix 2 x+y=6. Let an ellipse E: x^2/a^2+y^2/b^2=1, a>b, of eccentricity 1/(√ 2) pass through the focus…

Let $\displaystyle P$ be a parabola with vertex $\displaystyle (2,3)$ and directrix $\displaystyle 2 x+y=6$. Let an ellipse $\displaystyle E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$, of eccentricity $\displaystyle \frac{1}{\sqrt{2}}$ pass through the focus of the parabola $\displaystyle P$. Then, the square of the length of the latus rectum of $\displaystyle E$, is