JEE Main 2022 (Online) 24th June Evening Shift

Numerical

-1

Let the hyperbola $$H:{{{x^2}} \over {{a^2}}} - {y^2} = 1$$ and the ellipse $$E:3{x^2} + 4{y^2} = 12$$ be such that the length of latus rectum of H is equal to the length of latus rectum of E. If $${e_H}$$ and $${e_E}$$ are the eccentricities of H and E respectively, then the value of $$12\left( {e_H^2 + e_E^2} \right)$$ is equal to ___________.

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JEE Main 2021 (Online) 27th August Evening Shift

Numerical

-1

Out of Syllabus

Let A (sec$$\theta$$, 2tan$$\theta$$) and B (sec$$\phi$$, 2tan$$\phi$$), where $$\theta$$ + $$\phi$$ = $$\pi$$/2, be two points on the hyperbola 2x² $$-$$ y² = 2. If ($$\alpha$$, $$\beta$$) is the point of the intersection of the normals to the hyperbola at A and B, then (2$$\beta$$)² is equal to ____________.

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JEE Main 2021 (Online) 25th February Morning Shift

Numerical

-1

The locus of the point of intersection of the lines $$\left( {\sqrt 3 } \right)kx + ky - 4\sqrt 3 = 0$$ and $$\sqrt 3 x - y - 4\left( {\sqrt 3 } \right)k = 0$$ is a conic, whose eccentricity is _________.

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