Completing the Square for Quadratics

The circle with equation $(x - 1)^2 + y^2 = 4$ intersects the parabola $y = x^2 - 2x + 3$ in one location on the real $xy$ plane. Which of the following vertical translations is the smallest one we can apply to the parabola for which all intersections of the circle and parabola on the real $xy$ plane have the same $y$-coordinate?