If i have the equation of a circle and the equation of a line how do i show if the line is a tangent of the circle? At first i tried rearranging them both in the form f(x) = 0, setting them to equal each other. Rearranging and simplifying, then eliminating x or y by using the linear line equation. I was then going to try to find the points at which they meet and hence differentiate both equations to find dy/dx at this point - if they were equal i would have shown it was a tangent. However, this usually doesn't work. I'm not sure if there's something wrong with my algebraic manipulation but it's rarely solvable with the quadratic equation. Is there an easier way? If so, what is it?