The equation of a chord of the circle $x^{2} + y^{2} - 4 x = 0$ which is bisected at the point $(1, 1)$ is

x + y = 2

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3 x - y = 2

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x - 2 y + 1 = 0

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x - y = 0

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Solution

The correct option is D $x - y = 0$
Required equation of chord with $(1, 1)$ as mid point is given by,
$T = S_{1}$
$\Rightarrow x (1) + y (1) - 2 (x + 1) = 1^{2} + 1^{2} - 4 (1)$
$\Rightarrow y - x = 0$

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