jee-main 2025 Q9

jee-main · India · session1_22jan_shift2 Conic sections Triangle or Quadrilateral Area and Perimeter with Foci

Let $\mathrm { P } ( 4,4 \sqrt { 3 } )$ be a point on the parabola $y ^ { 2 } = 4 \mathrm { a } x$ and PQ be a focal chord of the parabola. If M and $N$ are the foot of perpendiculars drawn from $P$ and $Q$ respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :
(1) $17 \sqrt { 3 }$
(2) $\frac { 263 \sqrt { 3 } } { 8 }$
(3) $\frac { 34 \sqrt { 3 } } { 3 }$
(4) $\frac { 343 \sqrt { 3 } } { 8 }$

Let $\mathrm { P } ( 4,4 \sqrt { 3 } )$ be a point on the parabola $y ^ { 2 } = 4 \mathrm { a } x$ and PQ be a focal chord of the parabola. If M and $N$ are the foot of perpendiculars drawn from $P$ and $Q$ respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to :\\
(1) $17 \sqrt { 3 }$\\
(2) $\frac { 263 \sqrt { 3 } } { 8 }$\\
(3) $\frac { 34 \sqrt { 3 } } { 3 }$\\
(4) $\frac { 343 \sqrt { 3 } } { 8 }$

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