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JEE Main20206 Sep 2020Evening ShiftMathematicsParabolaActual

The centre of the circle passing through the point 0 , 1 and touching the parabola y = x 2 at the point 2 , 4 is :

Options

  1. A- 53 10 ,   16 5
  2. B6 5 ,   53 10
  3. C3 10 ,   16 5
  4. D- 16 5 ,   53 10

Correct answer

D. - 16 5 ,   53 10

Step-by-step solution

y = x 2 Tangent at 2 , 4 is 1 2 y + 4 = 2 x , using Cartesian form. ⇒ 4 x - y - 4 = 0 Equation of circle x - 2 2 + y - 4 2 + λ 4 x - y - 4 = 0 It passes through 0 , 1 ∴   4 + 9 + λ 0 - 1 - 4 = 0 13 = 5 λ ⇒ λ = 13 5 ∴ Circle is x 2 - 4 x + 4 + y 2 - 8 y + 16 + 13 5 4 x - y - 4 = 0 ⇒ x 2 + y 2 + 52 5 - 4 x - 8 + 13 5 y + 20 - 52 5 = 0 ⇒ x 2 + y 2 + 32 5 x - 53 5 y + 48 5 = 0 ∴ Centre is - 16 5 , 53 10

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