Coordinate Geometry: JEE Main 2026 Mathematics question

Let $y=x$ be the equation of a chord of the circle $C_1$ (in the closed half-plane $x\ge0$) of diameter 10 passing through the origin. Let $C_2$ be another circle described on the given chord as its 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