The number of common tangents to the circles $x^{2}+y^{2}=4$ and $x^{2}+y^{2}-6 x-8 y=24$ is

The centres of the given circles $x^{2}+y^{2}=4$ and $x^{2}+y^{2}-6 x-8 y=24$ are $C_{1}(0,0)$ and $\mathrm{C}_{2}(3,4)$ respectively. Their radii are $\mathrm{r}_{1}=2$ and $r_{2}=7$ respectively. $\mathrm{C}_{1} \mathrm{C}_{2}=5 < $ sum of radii But $C_{1} C_{2}=$ difference of radii Thus, the given circles touch each other internally. Hence, number of common tangent is only one.