Let E: x²/a² + y²/b² = 1, a > b and H: x²/A² - y²/B² = 1. Let the… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 22 January, Shift 2Conic Sections (Parabola, Ellipse, Hyperbola)

Let $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, \quad a > b \quad \text{and} \quad H: \frac{x^2}{A^2} - \frac{y^2}{B^2} = 1.$ Let the distance between the foci of $E$ and the foci of $H$ be $2\sqrt{3}$ . If $a - A = 2$ , and the ratio of the eccentricities of $E$ and $H$ is $\frac{1}{3}$ , then the sum of the lengths of their latus rectums is equal to:

A
$9$
B
$10$
C
$8$
D
$7$

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