1. The problem statement, all variables and given/known data Show that [itex]x+2y=7[/itex] is a tangent to the circle [itex]x^2+y^2-4x-1=0[/itex] 2. Relevant equations 3. The attempt at a solution One way would be to solve simultaneously by substituting for x or y and getting a perfect square showing that there is only one point of intersection. Is there any other way to do this? I was thinking about the idea that the angle made by a tangent and a radius is 90 degrees and that the product of the gradients of perpendicular lines is -1. Are such thoughts correct ones?