MathsJEE Main 28 Jan 2026, Shift 1·Q22·Numerical·Moderate

Conic Sections · Eccentricity and latus rectum

For some

\theta \in \left(0, \dfrac{\pi}{2}\right)

, let the eccentricity and the length of the latus rectum of the hyperbola

x^2 - y^2\sec^2\theta = 8

e_1

and

\ell_1

, respectively, and let the eccentricity and the length of the latus rectum of the ellipse

x^2\sec^2\theta + y^2 = 6

e_2

and

\ell_2

, respectively. If

e_1^2 = e_2^2\left(\sec^2\theta + 1\right)

, then

\left(\dfrac{\ell_1\ell_2}{e_1e_2}\right)\tan^2\theta

is equal to .

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