The intercept on the line $y = x$ by the circle $x^{2} + y^{2} - 2 x = 0$ , is $A B$ . The equation of the circle on $A B$ as a diameter, is

x^{2} + y^{2} = x + y

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x^{2} + y^{2} - x + y = 0

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x^{2} + y^{2} + x + y = 0

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x^{2} + y^{2} + x = y

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Solution

The correct option is B $x^{2} + y^{2} = x + y$
Solving given line and the circle,
$x^{2} + x^{2} - 2 x = 0 \Rightarrow x = 0, 1$
Thus coordinates of A and B are $(0, 0)$ and $(1, 1)$ respectively,
Hence equation of circle with AB as diameter is given by,
$x (x - 1) + y (y - 1) = 0 \Rightarrow x^{2} + y^{2} = x + y$

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