The equation of the circle passing through (1 | vedclass

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(C) For a circle passing through two points to have the smallest possible radius,the line segment joining these two points must be the diameter of the

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$x^2 + y^2 - x - y = 0$

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(C) For a circle passing through two points to have the smallest possible radius,the line segment joining these two points must be the diameter of the circle.Given points are $A(1, 0)$ and $B(0, 1)$.The equation of a circle with diameter endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $(x - x_1)(x - x_2) + (y - y_1)(y - y_2) = 0$.Substituting the given points:$(x - 1)(x - 0) + (y - 0)(y - 1) = 0$$x(x - 1) + y(y - 1) = 0$$x^2 - x + y^2 - y = 0$$x^2 + y^2 - x - y = 0$

The equation of the circle passing through $(1,0)$ and $(0,1)$ and having the smallest possible radius is:

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