Question 67
On the Cartesian plane $Oxy$ the parabola $y = x^2 - 2bx + a + 1$ meets the $x$-axis at points $A$ and $B$, and meets the $y$-axis at point $C$ (distinct from the origin). It appears that the point with the coordinates $(a, b)$ is a center of the circumscribed circle of the triangle $ABC$.
Find all possible values of the numbers $a$ and $b$.
(V. Karamzin)
Find all possible values of the numbers $a$ and $b$.
(V. Karamzin)