JEE Main 2022 (Online) 26th June Morning Shift | Parabola Question 65 | Mathematics

Let the common tangents to the curves $$4({x^2} + {y^2}) = 9$$ and $${y^2} = 4x$$ intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and l respectively denote the eccentricity and the length of the latus rectum of this ellipse, then $${l \over {{e^2}}}$$ is equal to ______________.

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JEE Main 2022 (Online) 24th June Evening Shift

Numerical

-1

Let P₁ be a parabola with vertex (3, 2) and focus (4, 4) and P₂ be its mirror image with respect to the line x + 2y = 6. Then the directrix of P₂ is x + 2y = ____________.

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JEE Main 2021 (Online) 31st August Evening Shift

Numerical

-1

Out of Syllabus

A tangent line L is drawn at the point (2, $$-$$4) on the parabola y² = 8x. If the line L is also tangent to the circle x² + y² = a, then 'a' is equal to ___________.

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JEE Main 2021 (Online) 20th July Evening Shift

Numerical

-1

If the point on the curve y² = 6x, nearest to the point $$\left( {3,{3 \over 2}} \right)$$ is ($$\alpha$$, $$\beta$$), then 2($$\alpha$$ + $$\beta$$) is equal to _____________.

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