Let Hₙ: x²/(1 + n) - y²/(3 + n) = 1, n ∈ ℕ. Let k be the smallest… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 11 April, Shift 1Conic Sections (Parabola, Ellipse, Hyperbola)

Let $H_n : \frac{x^2}{1 + n} - \frac{y^2}{3 + n} = 1$ , $n \in \mathbb{N}$ . Let $k$ be the smallest even value of $n$ such that the eccentricity of $H_k$ is a rational number. If $l$ is the length of the latus rectum of $H_k$ , then $21\,l$ is equal to:

A
$306$
B
$102$
C
$51$
D
$7$

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