3. Given $M=\left\{(x, y) \mid x^{2}+2 y^{2}=3\right\}, N=\{(x, y) \mid y=m x+b\}$. If for all $m \in \mathbf{R}$, we have $M \cap N \neq \varnothing$, then the range of $b$ is
A. $\left[-\frac{\sqrt{6}}{2}, \frac{\sqrt{6}}{2}\right]$
B. $\left(-\frac{\sqrt{6}}{2}, \frac{\sqrt{6}}{2}\right)$
C. $\left(-\frac{2}{3} \sqrt{3}, \frac{2}{3} \sqrt{3}\right)$
D. $\left[-\frac{2}{3} \sqrt{3}, \frac{2}{3} \sqrt{3}\right]$
3. $M \cap N=\varnothing$ is equivalent to the point $(0, b)$ being on the ellipse $\frac{x^{2}}{3}+\frac{2 y^{2}}{3}=1$ or inside it, hence $\frac{2}{3} b^{2} \leqslant 1 . b \in\left[-\frac{\sqrt{6}}{2}, \frac{\sqrt{6}}{2}\right]$