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JEE Main20203 Sep 2020Evening ShiftMathematicsParabolaActual

Let the latus rectum of the parabola y 2 = 4 x be the common chord to the circles C 1 and C 2 each of them having radius 2 5 . Then, the distance between the centres of the circles C 1 and C 2 is :

Options

  1. A12
  2. B8
  3. C8 5
  4. D4 5

Correct answer

B. 8

Step-by-step solution

Co-ordinates of focus of parabola will be S = a ,   0 = 1 ,   0 . Now, length of latus-rectum = 4 . So, length of semi latus-rectum = 2 . Also, ∠ L S C 1 = 90 ° Now, radius of circle L C 1 = 2 5 Now, applying pythagoras theorem in △ L S C 1 , L C 1 2 = C 1 S 2 + L S 2 ⇒ C 1 S 2 = L C 1 2 - L S 2 = 2 5 2 - 2 2 = 16 ⇒ C 1 S = 16 = 4 ∴ C 1 C 2 = 2 C 1 S = 2 × 4 = 8 .

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