3. Given the circle $M: 2 x^{2}+2 y^{2}-8 x-8 y-1=0$, and the line $l: x+y-9=0$, a point $A$ on $l$ is used to construct $\triangle A B C$ such that $\angle B A C=\frac{\pi}{4}$, with side $A B$ passing through the center $M$ of the circle, and $B, C$ on the circle $M$. Then the range of the y-coordinate of point $A$ is $\qquad$
3. $[3,6]$ Detailed Explanation: Let $A(a, 9-a)$, then the distance from $M$ to $AC$ is $d=|AM| \sin \frac{\pi}{4}, \because AC$ intersects the circle, $\therefore d \leqslant r=\sqrt{\frac{17}{2}}$, i.e., $AM \leqslant \sqrt{17}$. From $\sqrt{(a-2)^{2}+(7-a)^{2}} \leqslant \sqrt{17}$, we get $a^{2}-9 a+18 \leqslant 0 \Rightarrow 3 \leqslant a \leqslant 6, \therefore$ the range of the y-coordinate of point $A$ is $[3,6]$.