# Collisions in 2D

I'm designing a program that simulates collisions in 2 dimensions, among other things. The collisions are between 2 circles, the collisions themselves are perfectly elastic. The mass of the two circles are known, and their X and Y velocity components are known. They also have specific radii. I can easily detect collisions amongst 2 circles, but I cannot solve for the final Vx or Vy vectors of the two spheres.

Any help would be greatly appreciated.
Thanks