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Two curves y 2 = 4 a x and a y 2 - 4 x 3 = 0 , where a > 0 intersect each other at a point P in first quadrant. Normals are drawn to the curves at P , If they meet x -axis at A   &   B then mid point of A B is

Options

  1. A4 a , 0
  2. B5 a , 0
  3. C6 a , 0
  4. D7 a , 0

Correct answer

B. 5 a , 0

Step-by-step solution

The two curves intersect at a ,   2 a and a , – 2 a But P = a ,   2 a equation of normal to y 2 = 4 a x   a t   a ,   2 a is: y   – 2 a = – x   – a and equation of normal to a y 2 = 4   x 3 at a ,   2 a is: y – 2 a = – 1 3   x - a ∴   A = 3 a ,   0 and B = 7 a , 0 ∴ Mid point of A B = 5 a , 0

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