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JEE Main202324 Jan 2023Evening ShiftMathematicsParabolaActual

The equations of sides A B and A C of a triangle A B C are λ + 1 x + λ y = 4 and λ x + 1 - λ y + λ = 0 respectively. Its vertex A is on the y - axis and its orthocentre is 1 , 2 . The length of the tangent from the point C to the part of the parabola y 2 = 6 x in the first quadrant is

Options

  1. A6
  2. B2 2
  3. C2
  4. D4

Correct answer

B. 2 2

Step-by-step solution

Given, The equations of sides A B and A C of a triangle A B C and have orthocentre at 1 , 2 So, A B ≡ λ + 1 x + λ y = 4   . . . . . . . . 1 And A C ≡ λ x + 1 - λ y + λ = 0   . . . . . . 2 Also given vertex A is on the y - axis So, putting the value x = 0 in equation 1   &   2 we get, y = 4 λ   &   y = λ λ - 1 ⇒ 4 λ = λ λ - 1 ⇒ λ = 2 Now putting the value of λ in both equation we get, A B &#

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