jee_main_2026_28_january_morning - Conic Sections Topics

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QUESTION #22 Ellipse and Hyperbola
For some θ in (0, (π)/(2)), let the eccentricity and the length of the latus rectum of the hyperbola x² - y² ² θ = 8 be e₁ and ₁, respectively, and let the eccentricity and the length of the latus rectum of the ellipse x² ² θ + y² = 6 be e₂ and ₂, respectively. If e₁² = e₂² ( ² θ + 1), then (( ₁ ₂)/(e₁ e₂)) ² θ is equal to ____.
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