If slope of the chord of hyperbola $2x^2-3y^2=6$ which is bisected at (5, 3) is $\frac{p}{q}$, where p and q are co-prime positive integers, then the value of $|p-q|$ is

Equation of chord is $\frac{x-5}{\cos \alpha }=\frac{y-3}{\sin \alpha }=r$

Point $(5+r\cos \alpha ,3+r\sin \alpha )$ of chord is one of its end point $2{(5+r\cos \alpha )}^2-3{(3+r\sin \alpha )}^2=6$

(5, 3) is midpoint of chord iff sum of roots = 0

$20\cos \alpha -18\sin \alpha =0$

$\frac{\cos \alpha }{9}=\frac{\sin \alpha }{10}\Rightarrow \tan \alpha =\frac{10}{9}=m$

$\therefore p-q=1$