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NTA Abhyas JEE Main2020MathematicsParabolaPractice

Let B and C are the points of intersection of the parabola x = y 2 and the circle y 2 + x - 2 2 = 8 . The perimeter (in units) of the triangle O B C , where O is the origin, is

Options

  1. A8
  2. B4 5
  3. C4 5 + 2
  4. D4 5 + 1

Correct answer

D. 4 5 + 1

Step-by-step solution

On solving x = y 2 and y 2 + x - 2 2 = 8 we get, x + x - 2 2 = 8 ⇒ x 2 - 3 x - 4 = 0 ⇒ x = - 1 , 4 ⇒ x = 4 (as x ≠ - 1 is rejected because it makes y not defined) ⇒ y 2 = 4 ⇒ y = ± 2 Let, B = 4 , - 2 ,   C = 4 , 2 Now, perimeter of ∆ O B C = 4 + 4 5 units

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