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JEE Main20252 Apr 2025Morning ShiftMathematicsParabolaActual

Let the focal chord P Q of the parabola y^2=4 x make an angle of 60^ with the positive x -axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y -axis at the point (0, ) , then 5 ^2 is equal to :

Options

  1. A15
  2. B25
  3. C30
  4. D20

Correct answer

A. 15

Step-by-step solution

60^ = 2 t -0 t ^2-1 = 3 t = 3 P (3,2 3 ) Circle : (x-1)(x-3)+(y-0)(y-2 3 )=0 at x=0 3+y^2-2 3 y=0 y = 3 = 5 ^2=15

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