The line x=8 is the directrix of the ellipse E:(x²)/(a²)+(y²)/(b²)=1 with the corresponding focus (2,0). If the tangent to E at the point P in the first quadrant passes through the point (0,4 3) and intersects the x -axis at Q, then (3PQ)² is equal to _ _ _ _ _ _.

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 1 Feb, Evening shift · Q32

JEE Main 20231 Feb, Evening shiftMathematicsHardCoordinate Geometry478× since 2002

The line

x=8

is the directrix of the ellipse

\mathrm{E}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1

with the corresponding focus

(2,0)

. If the tangent to

\mathrm{E}

at the point

\mathrm{P}

in the first quadrant passes through the point

(0,4\sqrt3)

and intersects the

x

-axis at

\mathrm{Q}

, then

(3\mathrm{PQ})^{2}

is equal to ____________.

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