The line is the radical axis.
Ok ,
Suppose you take two circles and they do not intersect:
e.g
x^2 + y^2 -6x-6y+14=0
x^2 +y^2 +6x+4y+12 =0
If you subtract the two equations you get a line:
-12x-10y+2=0
Now, if we chose any point P on this line, then the lengths of the tangents from P to each of the circles are equal?
Why and how do we prove this?
(I know that that if the intersected, the line would represent a common chord)
The line is the radical axis.