Let   be a circle. If two chords from   bisected by x-axis are drawn to the circle then the condition is

$$\begin{gathered} \mathrm{Chords} \mathrm{through} \left(\mathrm{a},1\right) \mathrm{are} \mathrm{bisected} \mathrm{on} \mathrm{x} \mathrm{axis} \\ \Rightarrow \mathrm{other} \mathrm{end} \mathrm{of} \mathrm{the} \mathrm{chord} \mathrm{is} \left(\mathrm{x},-1\right) \\ \mathrm{sub} \mathrm{in} \mathrm{the} \mathrm{circle} \\ \Rightarrow \mathrm{x}\left(\mathrm{x}-\mathrm{a}\right)+\left(-1\right)\left(-2\right)=0 \\ {\mathrm{x}}^2-\mathrm{ax}+2=0 \\ \mathrm{For} 2 \mathrm{chords} \mathrm{discriminant}>0 \\ \Rightarrow {\mathrm{a}}^2>8 \end{gathered}$$