Is a line ax+by+c=0 tangent to a circle?

Get a line a form y=-ax/b-c/b, then substitute into a cirle equation (x-p)^2 +(y-s)^2=r^2. Get a quadratic and find whether a discriminant is equal to zero. If it is then the line is tangent to a circle. Otherwise, for d>0 the line cuts through two points on a circle, for d<0 the line has no common points with a circle.