The ordinates of the points P and Q on the parabola with focus (3,0) and directrix x=-3 are in the ratio 3: 1. If R(α, β) is the point of intersection of the tangents to the parabola at P and Q, then (β²)/(α) is equal to _ _ _ _ _ _ _ _.

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q41

JEE Main 20238 Apr, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

The ordinates of the points P and

\mathrm{Q}

on the parabola with focus

(3,0)

and directrix

x=-3

are in the ratio

3: 1

. If

\mathrm{R}(\alpha, \beta)

is the point of intersection of the tangents to the parabola at

\mathrm{P}

and

\mathrm{Q}

, then

\frac{\beta^{2}}{\alpha}

is equal to _______________.

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