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If two parabolas y 2 = 4 a x – k and x 2 = 4 a y – k have only one common point P , then the equation of normal to y 2 = 4 a x – k at P is

Options

  1. Ay + x = 4 a
  2. By + x = 2 a
  3. Cy + x = 4
  4. Dy + x = 2

Correct answer

A. y + x = 4 a

Step-by-step solution

Parabolas y 2 = 4 a x – k and x 2 = 4 a y – k touche each other at line y = x ( ∵ both parabola are inverse of each other) ⇒ y = x is a common tangent at P ⇒ we get point P by solving y 2 = 4 a x – k and y = x ⇒ point of contact P is 2 a , 2 a ⇒ equation of normal at P 2 a , 2 a is x + y = 4 a

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