JEE Main 2024 — Mathematics Coordinate Geometry
Let P(α,β) be a point on the parabola y2=4x. If P also lies on the chord of the parabola x2=8y whose mid point is (1,45), then (α−28)(β−8) is equal to _______.
Held on 29 Jan 2024 · Verified 6 Jul 2026.
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Suppose that two chords, drawn from the point $(1, 2)$ on the circle $x^2 + y^2 + x - 3y = 0$ are bisected by the $y$-axis. If the other ends of these chords are $R$ and $S$, and the mid point of the line segment $RS$ is $(\alpha, \beta)$, then $6(\alpha + \beta)$ is equal to:
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If the line $\alpha x+4 y=\sqrt{7}$, where $\alpha \in \mathbf{R}$, touches the ellipse $3 x^{2}+4 y^{2}=1$ at the point P in the first quadrant, then one of the focal distances of $P$ is :
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