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Hyperbola question

2023 · 11 Apr · Shift 1 · Q42

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JEE Main
Mathematics
Hyperbola
2023 · 11 Apr · Shift 1 · Q42

Hyperbola question

2023 · 11 Apr · Shift 1 · Q42

JEE MainMathematicsHyperbolaNumerical+4 / −1

Let

\mathrm{H}_{\mathrm{n}}: \frac{x^{2}}{1+n}-\frac{y^{2}}{3+n}=1, n \in N

. Let

\mathrm{k}

be the smallest even value of

\mathrm{n}

such that the eccentricity of

\mathrm{H}_{\mathrm{k}}

is a rational number. If

l

is the length of the latus rectum of

\mathrm{H}_{\mathrm{k}}

, then

21 l

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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