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

Question

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, 2 k , 2 k, k , k, a , 2 k, k , 2 a

MARKS App · Accepted Answer

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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