A square is inscribed in a circle x^{2}+y^{2}+2x+2y+1=0 and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?

Explanation

The circle is (x+1)^2 + (y+1)^2 = 1, with center C(-1,-1) and radius r=1. For a square inscribed with sides parallel to axes, the vertices lie at an angle of 45^{\circ} to the axes from the center. The vertices are (x_c \pm r\cos 45^{\circ}, y_c \pm r\sin 45^{\circ}) = (-1 \pm \frac{1}{\sqrt{2}}, -1 \pm \frac{1}{\sqrt{2}}). Option (c) perfectly matches one of these points.

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