NTA Abhyas JEE Main2020MathematicsParabolaPractice

If two parabolas y 2 = 4 a x - k and x 2 = 4 a y - k have only one common point P, then the coordinates of P are

Options

A2 k , 2 k
Bk , k
Ca , 2 k
Dk , 2 a

Correct answer

A. 2 k , 2 k

Step-by-step solution

Parabolas y 2 = 4 a x - k and x 2 = 4 a y - k touch each other at the line y = x ( ∵ both parabolas are inverse of each other) ⇒ y = x is the common tangent at P ⇒ we get point P by solving y 2 = 4 a x - k and y = x ⇒ point of contact P = 2 a , 2 a ⇒ 2 a 2 = 4 a 2 a - k ⇒ k = a ⇒ P = 2 k , 2 k

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