Let the ellipse E_1: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b and E_2: \frac{x^2}{A^2}+\frac{y^2}{B^2}=1, A< B have same eccentricity {1}/{\sqrt{3}}. Let the product of their lengths of latus rectums be {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 A B C D equals [29 Jan 2025 Shift 1]

Ellipse

Section: Mathematics

Question : 20 of 110

Marks: +1, -0

Let the ellipse E1:‌

+‌

=1,a>b and E2:‌

+‌

=1,A<B have same eccentricity ‌

√3

. Let the product of their lengths of latus rectums be ‌

√3

, and the distance between the foci of E1 be 4 . If E1 and E2 meet at A,B,C and D, then the area of the quadrilateral ABCD equals

[29 Jan 2025 Shift 1]

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