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JEE Main202522 Jan 2025Evening ShiftMathematicsParabolaActual

Let P (4,4 3 ) be a point on the parabola y^2=4 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 :

Options

  1. A17 3
  2. B263 3 8
  3. C34 3 3
  4. D343 3 8

Correct answer

D. 343 3 8

Step-by-step solution

aligned & (4,4 3 ) lies on y^2=4 ax & 48=4 a 4 & 4 a =12 aligned y^2=12 x is equation of parabola Now, parameter of P is t₁= 2 3 Parameters of Q is t ₂=- 3 2 Q ( 9 4 ,-3 3 ) Area of trapezium PQNM aligned & = 1 2 MN ( PM + QN ) & = 1 2 MN ( PS + QS ) & = 1 2 MN PQ & = 1 2 7 3 49 4 =(343) 3 8 aligned

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