Just solve the system




by substitution

Substitute 2Y for X in the first:










Divide every term by 5



Factor:

(Y-3)(Y-3)=0

 gives 
 gives 

[The fact that we get only one solution tells us
that the line touches the circle in only one
point. So this proves that it is indeed tangent]

Now to find 

Substitute  for  in




6=X

So the point of tangency is (6,3)

Edwin