Question

Let C be the locus of the mirror image of a point on the parabola y² = 4x with respect to the line y = x. Then the equation of tangent to C at P(2,1) is :

(1) x – y = 1

(2) 2x + y = 5

(3) x + 3y = 5

(4) x + 2y = 4

Answer 1

Correct answer is (1)

Given y² = 4x

Mirror image on y = x

\(\Rightarrow\) C : x² = 4y

Equation of tangent at (2, 1)

\(\Rightarrow\) y – 1 = 1(x – 2)

\(\Rightarrow\) x – y = 1