The equation of the circle passing through the points (1,0) and (0,1) and having the smallest radius is:
Solutions · 1
Official solution
Among all circles through two fixed points, the one with smallest radius has that chord as its diameter. Circle on (1,0),(0,1) as diameter:
\[(x-1)(x-0)+(y-0)(y-1)=0\Rightarrow x^2+y^2-x-y=0.\]