The correct option is C a2 > 8
The equation of the circle is x2 + y2 -ax -ay = 0
Let (x, 0) be the midpoint of a chord drawn the point (a, 1)
Then the equation of the chord bisected at (x1, 0) is xx1−92(x+x1)−12(y+0)=x21−ax1
⇒2x21−2ax1=2x1x−ax−ax1−y.
The chord passes through (a, 1)
⇒2x21−3ax1+a2+1=0
x1 is real ⇒9a2−4(2)(a2+1)>0 ⇒9a2−8as−8> 0 ⇒a2 > 8