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JEE Main201912 Apr 2019Evening ShiftMathematicsParabolaActual

The tangents to the curve y = x - 2 2 - 1 at its points of intersection with the line x - y = 3 , intersect at the point:

Options

  1. A5 2 , 1
  2. B5 2 , - 1
  3. C- 5 2 , - 1
  4. D- 5 2 , 1

Correct answer

B. 5 2 , - 1

Step-by-step solution

Let coordinates of C be h , k chord of contact of C w. r. t. y = x - 2 2 - 1 ⇒ y = x 2 - 4 x + 3 is T = 0 y + k 2 = x h + 3 - 2 x + h ⇒ 2 h - 2 x - y = - 6 - 4 h - k   compare it with x - y = 3 2 h - 2 = 1 ⇒ h = 5 2 6 - 4 h - k = - 3   ⇒ k = - 1 ∴   C is 5 2 , - 1

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