Consider the circles x^2+y^2=1 and x^2+y^2-2x-6y+6=0. Then find the equation of a common tangents to a circles ???

Answer 1

the line joining the two centers is y=3x
the two tangents cross midway between where the line intersects the circles.
Now find where a line with slope -1/y' goes through that point.

Or, google the problem and I'm sure you will find a more general method.

Answer 2

My answer is 4x-3y-5=0

Answer 3

Ignore my previous post. But I don't think your equation is right either.
Consider that the two circles have
center (0,0) radius=1
center (1,3) radius=2
Then one common tangent is the line y=1
So the other will have negative slope, not a slope of 4/3

Answer 4

wow - my bad. I was thinking only of the internal tangents.
Good job.