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JEE Main202124 Feb 2021Evening ShiftMathematicsParabolaActual

If P is a point on the parabola y = x 2 + 4 which is closest to the straight line y = 4 x - 1 , then the co-ordinates of P are:

Options

  1. A- 2 , 8
  2. B1 , 5
  3. C2 , 8
  4. D3 , 13

Correct answer

C. 2 , 8

Step-by-step solution

P : y = x 2 + 4 k = h 2 + 4 L : y = 4 x - 1 y - 4 x + 1 = 0 D = A B = k - 4   h + 1 17 = h 2 + 4 - 4   h + 1 17 d D d h = 2   h - 4 17 = 0 h = 2 d 2 D d h 2 = 2 17 > 0 ∴ k = 4 + 4 = 8 ∴ Point 2 , 8

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