Explanation

(b)
Let the points be $A = (2,\ 2)$and$B = (3,\ 3)$. Since the circle passing through these points, so they satisfy the equation of the circle.
Now, taking option (b),
Let $S \equiv x^{2} + y^{2} - 5x - 5y + 12 = 0$
At $A\text{=}(2,\ 2)$
$2^{2} + 2^{2} - 5(2) - 5(2) + 12 = 0$
At $B = (3,\ 3)$
$3^{2} + 3^{3} - 5(3) - 5(3) + 12 = 0$