JEE Math Practice Question

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

1. A.$$\frac{512}{25}$$
2. B.$$\frac{656}{25}$$
3. C.$$\frac{385}{8}$$
4. D.$$\frac{347}{8}$$