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Question

(B) The smallest circle passing through two points $A(x_1, y_1)$ and $B(x_2, y_2)$ has the line segment $AB$ as its diameter.Given points are $A(2,2)$

Vedclass · Accepted Answer

$x^{2}+y^{2}-5x-5y+12=0$

Vedclass · Answer

(B) The smallest circle passing through two points $A(x_1, y_1)$ and $B(x_2, y_2)$ has the line segment $AB$ as its diameter.Given points are $A(2,2)$ and $B(3,3)$.The equation of the circle with diameter $AB$ is given by $(x-x_1)(x-x_2) + (y-y_1)(y-y_2) = 0$.Substituting the coordinates,we get $(x-2)(x-3) + (y-2)(y-3) = 0$.Expanding this,we have $(x^2 - 5x + 6) + (y^2 - 5y + 6) = 0$.Simplifying,we get $x^2 + y^2 - 5x - 5y + 12 = 0$.Thus,option $B$ is correct.

The equation of the smallest circle passing through the points $(2,2)$ and $(3,3)$ is

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