2. Find the common tangent line equation of the curves $9 x^{2}+16 y^{2}=144$ and $7 x^{2}-32 y^{2}=224$.
2. The standard equations of the curves are $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ and $\frac{x^{2}}{32}-\frac{y^{2}}{7}=1$. By the necessary and sufficient condition for a line to be tangent to both curves, we have

thus, the equations of the common tangents are $x+y \pm 5=0$ and $x-y \pm 5=0$.