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JEE Main20199 Apr 2019Evening ShiftMathematicsParabolaActual

The area (in sq. units) of the smaller of the two circles that touch the parabola, y 2 = 4 x at the point 1 , 2 and the x -axis is

Options

  1. A8 π 3 - 2 2
  2. B8 π 2 - 2
  3. C4 π 3 + 2
  4. D4 π 2 - 2

Correct answer

A. 8 π 3 - 2 2

Step-by-step solution

The equation of the tangent to the parabola y 2 = 4 a x at x 1 ,   y 1 is y y 1 = 2 a x + x 1 . Equation of tangent to the parabola y 2 = 4 x at 1 ,   2 is y ⋅ 2 = 2 x + 1 ⇒ x - y + 1 = 0       . . . i The equation of the family of circles touching a line l = 0 at x 1 ,   y 1 is x - x 1 2 + y - y 1 2 + λ l = 0 . Equation of family of circle touching the parabola at 1 ,   2 is x - 1 2 + y - 2 2 + λ x - y + 1 = 0       . . . i i Since circle touc

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