Mathematics Question from JEE Main 2026 · 28 January, Shift 1

Let $y = x$ be the equation of a chord of the circle $C_1$ (in the closed half-plane $x \ge 0$) of diameter $10$ passing through the origin. Let $C_2$ be another circle described on the given chord as diameter. If the equation of the chord of the circle $C_2$, which passes through the point $(2, 3)$ and is farthest from the center of $C_2$, is $x + ay + b = 0$, then $a - b$ is equal to: