Circle

Point of intersection of direct common tangents is (6, 0).

Let the equation of common tangent be
y - 0 = m(x - 6)
as it touches x2+y2 = 4.
⇒ |

0−0+6m

√1+m2

| = 2
9m2 = 1+m2
m = ±

1

2√2

So, the equation of common tangent is
y =

1

2√2

(x - 6), y = −

1

2√2

(x−6) and also x = 2.