the number of common tangents to the circle x2 +y2 =4
and the circle
x2 + y2 -6x-8y =24 is
x2 + y2 -6x - 8y =24
Circle 1 has center as (0,0) and radius 2
Circle 2 has center as (3,4 ) and radius 7
If you plot both circles , they will intersect each other.
So only two common tangents can be drawn. If they only touch each other , then there will be 3 tangents.
For two intersecting circles, there are two common tangents always.