Two distinct chords drawn from the point (p, q) on the circle $x^2+y^2=px+qy$, where $pq\ne 0$ are bisected by the $x-axis$. Then  

Suppose chord bisect at $M(\lambda ,0)$ , then other end point of chord is $(h,-q)$ where $\lambda =\frac{p+h}{2}$

Which lie on $x^2+y^2=px+qy$ or $h^2+q^2=ph-q^2$$\Rightarrow h^2-ph+2q^2=0$

for two chords, $\mathrm{\Delta }>0\Rightarrow p^2-\mathrm{4.1.2}{q}^2<0\Rightarrow p^2>8q^2$