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Ellipse question

2025 · 29 Jan · Shift 1 · Q30

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PYQ Library
JEE Main
Mathematics
Ellipse
2025 · 29 Jan · Shift 1 · Q30

Ellipse question

2025 · 29 Jan · Shift 1 · Q30

JEE MainMathematicsEllipseMCQ+4 / −1

Let the ellipse

E_1: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1

,

a \gt b

and

E_2: \frac{x^2}{A^2} + \frac{y^2}{B^2} = 1

,

A \lt B

have same eccentricity

\frac{1}{\sqrt{3}}

. Let the product of their lengths of latus rectums be

\frac{32}{\sqrt{3}}

and the distance between the foci of

E_1

be 4. If

E_1

and

E_2

meet at A, B, C and D, then the area of the quadrilateral ABCD equals :

A
$\frac{24\sqrt{6}}{5}$
B
$\frac{18\sqrt{6}}{5}$
C
$6\sqrt{6}$
D
$\frac{12\sqrt{6}}{5}$

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