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JEE Main202529 Jan 2025Morning ShiftMathematicsParabolaActual

Two parabolas have the same focus ((4,3) ) and their directrices are the (x )-axis and the (y )-axis, respectively. If these parabolas intersects at the points (A ) and (B ), then ((A B)^2 ) is equal to :

Options

  1. A392
  2. B384
  3. C192
  4. D96

Correct answer

C. 192

Step-by-step solution

The parabolas are (x-4)^2+(y-3)^2=x^2 ...(i) and (x-4)^2+(y-3)^2=y^2 ... If point of intersection are A (x₁, y₁ ) and B (x₂, y₂ ) By solving (i) and (ii), we get aligned & x₁+x₂=14 and x₁ x₂=25 & (A B)^2=2 ( (x₁+x₂ )^2-4 x₁ x₂ )=192 aligned

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