Calculus question involving implicit differentiation.?

Lets say we had an equation to implicitly solve x^2+y^2 = 25, I know how to find the derivative but when the question is to find where there are vertical or horizontal tangents I have no idea what to do. I guess with horizontal tangents you solve for the numerator = 0 and for vertical tangents you have denominator = 0 except I don't understand what is going on with a couple steps down replacing the original equation with what you get and I have no idea what to do from there. Thanks for the help, I really appreciate it.