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 point P(2,1) is

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$x - y = 1$

$2 x + y = 5$

$x + 3 y = 5$

$x + 2 y = 4$

answer is A.

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Detailed Solution

${Equation of mirror image of a point on y}^{2} {=4x is x}^{2} =4y' C' is x^{2} = 4 y, tangent at P (2, 1) is S_{1} = 0 \Rightarrow x (2) = 2 (y + 1) \Rightarrow x - y = 1$

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