Official solution
For this circle
x 2 + y2 = 4
Center C1 = (0, 0) and radius r1 = 2
For this circle
x2 + y2 + 6x + 8y -- 24 = 0
Center C2 = (-3, -4) and radius r2 = \[\sqrt {9 + 16 + 24} \] = 7
So distance between center,
C1C2 = 5
r1 + r2 = 7
|r1 - r2| = 5
As C1C2 = |r1 - r2|
\[ \therefore \] Circles touches internally.
Here Equation of common tangent is same as common chord.
\[ \therefore \] S1 - S2 = 0
\[ \Rightarrow \] (x 2 + y2 - 4) - (x2 + y2 + 6x + 8y - 24) = 0
\[ \Rightarrow \] - 6x - 8y + 20 = 0
\[ \Rightarrow \] 3x + 4y - 10 = 0
By checking all the options you can see that,
(6, --2) point satisfy the equation 3x + 4y - 10 = 0.