A square is inscribed in the circle x^2 + y^2 | vedclass

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(D) The equation of the circle is $x^2 + y^2 - 2x + 4y + 3 = 0$.Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -1$ a

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None of these

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(D) The equation of the circle is $x^2 + y^2 - 2x + 4y + 3 = 0$.Comparing this with the general form $x^2 + y^2 + 2gx + 2fy + c = 0$,we get $g = -1$ and $f = 2$.The center of the circle is $(-g, -f) = (1, -2)$ and the radius $r = \sqrt{g^2 + f^2 - c} = \sqrt{(-1)^2 + 2^2 - 3} = \sqrt{1 + 4 - 3} = \sqrt{2}$.Since the sides of the square are parallel to the coordinate axes,the vertices of the square are at a distance $r$ from the center along the diagonals.The vertices are $(1 \pm r \cos(45^\circ), -2 \pm r \sin(45^\circ)) = (1 \pm \sqrt{2} \cdot \frac{1}{\sqrt{2}}, -2 \pm \sqrt{2} \cdot \frac{1}{\sqrt{2}}) = (1 \pm 1, -2 \pm 1)$.The vertices are $(2, -1), (0, -1), (0, -3), (2, -3)$.Comparing these with the given options,none of the options match the calculated vertices.Therefore,the correct option is $(d)$.

$A$ square is inscribed in the circle $x^2 + y^2 - 2x + 4y + 3 = 0$,whose sides are parallel to the coordinate axes. One vertex of the square is

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