The given circle is S=x2+y2−ax−b@y=0
Since the two chords are bisected by x-axis so let (h,0) be the mid-point where h has two real values.
Equation of the chord by T=S2 is
x.h+y.0−a2(x+h)−b4(y+0)=h2−ah.
It passes through (a,b/2)
∴ah−a2(a+h)−b4(b2)=h2−ah.
or h2−32ah+(a22+b28)=0
Since the values of h are real and distinct we must have B2−4AC>0
∴94a2−4(a22b28)>0 or a2>2b2.