2. C

From the graph, we immediately obtain $\left\{\begin{array}{l}m+2 \geqslant \frac{3}{4} \\ m-2 \leqslant \frac{3}{4}\end{array}\right.$, so $-\frac{5}{4} \leqslant m \leqslant \frac{11}{4}$.
2. Given $\left.M=|(x, y)| 3 x^{2}+4 y^{2}-6 m x+3 m^{2}-12=0\right\}, N=\{(x, y) \mid$ $2 y^{2}-12 x+9=0$ If $M \cap N \neq \phi$, then the range of values for $m$ is ( ).
A. $m \geqslant-\frac{5}{4}$
B. $-\frac{5}{4} \leqslant m \leqslant \frac{13}{4}$
C. $-\frac{5}{4} \leqslant m \leqslant \frac{11}{4}$
1). $-1<m \leqslant \frac{13}{4}$