Find the equations of a circle passing through the points (1, 1), (2, 2) and whose radius is 1 unit:
a) (x-1)² + (y-1)² = 1
b) (x-2)² + (y-2)² = 1
c) x² + y² = 1
d) (x+1)² + (y+1)² = 1