Let $A(a,b)$, $B(3,4)$ and $C(-6,-8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2a+3,\ 7b+5)$ from the line $2x+3y-4=0$ measured parallel to the line $x-2y-1=0$ is: