Let (t,m) be the other end of the chord drawn from the point (p,q) on the circle x2+y2=px+qy Their mid-point is (
t+p
2
,
m+q
2
) Since, mid-point lies on X -axis i.e. y=0 m+q=0 ..........(i) Also, (t,m) lies on the circle. ∴t2+m2−pt−qm=0 ..........(ii) From Eqs. (i) and (ii), we get t2−pt+2q2=0 Which is quadratic in t such that, Discriminant >0 ⇒p2−8q2>0⇒p2>8q2