VITEEE 2011 Paper

The centres of the given circles x2+y2 = 4 and x2+y2 - 6x - 8y = 24 are C1 (0, 0) and C2 (3,4) respectively.
Their radii are r1 = 2 and r2 = 7 respectively.
C1C2 = 5 < sum of radii
But C1C2 = difference of radii
Thus, the given circles touch each other internally.
Hence, number of common tangent is only one.