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

The centres of the two circles are $C_1(0,0)$ and $C_2(3,4)$, and their radii are 2 and 7 respectively.

We have, $C_1{C}_2=5<$ Sum of the radii.

Also, $C_1{C}_2=$ Difference of the radii

Thus, the two circles touch each other internally. Hence, there is only one common tangent.