the centre of is (0,0)
the centre of is (6,3)
Distance from (0,0) to (6,3) is
hence the circles touch 2 thirds of the way from (0,0) to (6,3) which is (4,2)
the equation of the line from (0,0) to (6,3) is
the tangent line at the point of contact is perpendicular to this line
(slopes multiply to give -1) and contains the point (4,2)
You can then write the equation of this line.
now subtract the circle equations having multiplied out the factors in one of them.
compare your two answers.