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Ellipse question

2024 · 31 Jan · Shift 2 · Q36

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JEE Main
Mathematics
Ellipse
2024 · 31 Jan · Shift 2 · Q36

Ellipse question

2024 · 31 Jan · Shift 2 · Q36

JEE MainMathematicsEllipseMCQ+4 / −1

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

A
$\frac{512}{25}$
B
$\frac{656}{25}$
C
$\frac{385}{8}$
D
$\frac{347}{8}$

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