Coordinate Geometry: JEE Main 2026 Mathematics question

If the points of intersection of the ellipses $x^2+2y^2-6x-12y+23=0$ and $4x^2+2y^2-20x-12y+35=0$ lie on a circle of radius $r$ and centre $(a, b)$, then the value of $ab+18r^2$ is