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Jee Main 2025 — Medium JEE math MCQ

Let $P(4, 4\sqrt{3})$ be a point on the parabola $y^2 = 4ax$ 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. A. \( 17\sqrt{3} \)
  2. B. \( \frac{263\sqrt{3}}{8} \)
  3. C. \( \frac{34\sqrt{3}}{3} \)
  4. D. \( \frac{34\sqrt{3}}{8} \)

Solution

The correct option is **D**. (D. \( \frac{34\sqrt{3}}{8} \))

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let P(4,43)P(4, 4\sqrt{3}) be a point on the parabola y2=4axy^2 = 4ax and PQPQ be a focal chord of the parabola. If MM and NN are the foot of perpendiculars drawn from PP and QQ respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep