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(B) Let the vertices of the square be $(0,0), (1,0), (1,1),$ and $(0,1)$ in the $xy$-plane.Let the point be $P(x, y)$.The distances of $P$ from the fo

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(B) Let the vertices of the square be $(0,0), (1,0), (1,1),$ and $(0,1)$ in the $xy$-plane.Let the point be $P(x, y)$.The distances of $P$ from the four sides are $x, (1-x), y,$ and $(1-y)$.According to the problem,the sum of the squares of these distances is $9$:$x^2 + (1-x)^2 + y^2 + (1-y)^2 = 9$$x^2 + 1 - 2x + x^2 + y^2 + 1 - 2y + y^2 = 9$$2x^2 - 2x + 2y^2 - 2y + 2 = 9$$2x^2 - 2x + 2y^2 - 2y = 7$$x^2 - x + y^2 - y = \frac{7}{2}$This is the equation of a circle of the form $x^2 + y^2 + 2gx + 2fy + c = 0$.

The locus of a point which moves such that the sum of the squares of its distances from the sides of a square of side length $1$ is $9$,is

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