Coordinate Geometry: JEE Main 2026 Mathematics question

Suppose that two chords, drawn from the point $(1,2)$ on the circle $x^2+y^2+x-3y=0$ are bisected by the $y$-axis. If the other ends of these chords are R and S, and the mid point of the line segment RS is $(\alpha,\beta)$, then $6(\alpha+\beta)$ is equal to: