2. Given the line $L: x+y-9=0$ and the circle $M: 2 x^{2}+2 y^{2}-8 x-8 y-$ $1=0$, point $A$ is on line $L$, $B$ and $C$ are two points on circle $M$, in $\triangle A B C$, $\angle B A C=45^{\circ}, A B$ passes through the center of circle $M$, then the range of the x-coordinate of point $A$ is $\qquad$ .
(2) $3 \leqslant a \leqslant 6$ Hint: Let $A(a, 9-a)$, then the distance from the center $M$ to the line $A C$ is $d=|A M| \sin 45^{\circ}$. Since the line $A C$ intersects the circle $M$, we have $d \leqslant \frac{\sqrt{34}}{2}$, solving this yields $3 \leqslant a \leqslant 6$.