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Jee Main 2025 — Medium JEE math MCQ

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 \( \frac{1}{\sqrt{3}} \). 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:
  1. A. \quad 4\sqrt{6} \\
  2. B. \quad 6\sqrt{6} \\
  3. C. \quad 18\sqrt{6}/5 \\
  4. D. \quad 24\sqrt{6}/5 \\

Solution

The correct option is **D**. (D. \quad 24\sqrt{6}/5 \\ \end{align*} \])

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let the ellipse E1:x2a2+y2b2=1,a>b E_1 : \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, a > b and E2:x2A2+y2B2=1,A<B E_2 : \frac{x^2}{A^2} + \frac{y^2}{B^2} = 1, A < B have same eccentricity 13 \frac{1}{\sqrt{3}} . Let the product of their lengths of latus rectums be 323 \frac{32}{\sqrt{3}} , and the distance between the foci of E1 E_1 be 4. If E1 E_1 and E2 E_2 meet at A,B,C A, B, C and D D , then the area of the quadrilateral ABCD ABCD equals:
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep