We want the equation of the line with positive slope that is tangent two the two circles:

If you let be a point on

, then and it slope at x=a is .

Also, let be a point on

, then and its slope at x=b is

These slopes have to be the same, so setting them equal and solving for a we get ..........[1]

Just using the slope formula, the slope of AB is:

This has to be the same as the slope at A:

Sub in [1] and solve for b and we get:

This means that

This gives a slope of

So, we have two points and a slope. Almost there.

Using these we find we have a line equation of: