The equation of the circle passing through the point $(1,0)$ and $(0,1)$ and having the smallest radius is (1) $x^{2}+y^{2}-2x-2y+1=0$ (2) $x^{2}+y^{2}+2x+2y-7=0$ (3) $x^{2}+y^{2}-x-y=0$ (4) $x^{2}+y^{2}+x+y-2=0$
The equation of the circle passing through the point $(1,0)$ and $(0,1)$ and having the smallest radius is\\
(1) $x^{2}+y^{2}-2x-2y+1=0$\\
(2) $x^{2}+y^{2}+2x+2y-7=0$\\
(3) $x^{2}+y^{2}-x-y=0$\\
(4) $x^{2}+y^{2}+x+y-2=0$