Find the equation of the circle passing through (1, 0), (0, 1) and (1, 1).
Correct: A
The general equation of a circle is x^2 + y^2 + 2gx + 2fy + c = 0. Since it passes through (1, 0), (0, 1), (1, 1), we get 1 + 2g + c = 0, 1 + 2f + c = 0 and 1 + 2g + 2f + 2g + 2f + c = 0. Solve to get g = f = -1/2 and c = 0. So the equation is x^2 + y^2 - x - y = 0 or (x - 1/2)^2 + (y - 1/2)^2 = (1/2)^2 + (1/2)^2 = 1/2.