Let the tangent to the curve x²+2 x-4 y+9=0 at the point P(1,3) on it meet the y -axis at A. Let the line passing through P and parallel to the line x-3 y=6 meet the parabola y²=4 x at B. If B lies on the line 2 x-3 y=8, then (AB)² is equal to _ _ _ _ _ _.

Coordinate Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 6 Apr, Morning shift · Q43

JEE Main 20236 Apr, Morning shiftMathematicsHardCoordinate Geometry478× since 2002

Let the tangent to the curve

x^{2}+2 x-4 y+9=0

at the point

\mathrm{P}(1,3)

on it meet the

y

-axis at

\mathrm{A}

. Let the line passing through

\mathrm{P}

and parallel to the line

x-3 y=6

meet the parabola

y^{2}=4 x

\mathrm{B}

. If

\mathrm{B}

lies on the line

2 x-3 y=8

, then

(\mathrm{AB})^{2}

is equal to ___________.

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