Let one focus of the hyperbola H: x²/a² - y²/b² = 1 be at (√10, 0… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 2 April, Shift 1Conic Sections (Parabola, Ellipse, Hyperbola)

Let one focus of the hyperbola $H: \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ be at $\left(\sqrt{10}, 0\right)$ and the corresponding directrix be $x = \frac{9}{\sqrt{10}}$ . If $e$ and $l$ are respectively the eccentricity and the length of the latus rectum of $H$ , then $9(e^2 + l)$ is equal to:

A
$14$
B
$16$
C
$15$
D
$12$

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