Never mind, after reading my own post I think I have it. I noticed that since the points occur on the line y=x, then the x and y values will equal each other. So, I just re-wrote the original formula for the circle substituting x = y into it to get:
Which looks right. But I didn't really use implicit differentiation to find the two points did I? It was more geometry :S is there another way?
I hope I don't get that on my test