JEE Main202116 Mar 2021Evening ShiftMathematicsParabolaActual

Let C be the locus of the mirror image of a point on the parabola y 2 = 4 x with respect to the line y = x . Then the equation of tangent to C at P 2 , 1 is :

Options

Ax - y = 1
B2 x + y = 5
Cx + 3 y = 5
Dx + 2 y = 4

Correct answer

A. x - y = 1

Step-by-step solution

Given y 2 = 4 x Mirror image on y = x ⇒ C   :   x 2 = 4 y 2 x = 4 · d y d x ⇒ d y d x = x 2 d y d x P 2 , 1 = 2 2 = 1 Equation of tangent at 2 , 1 ⇒ y - 1 = 1 × x - 2 ⇒ x - y = 1

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