1. The problem statement, all variables and given/known data Hi there! In this exercise, we are supposed to derive this formula for a 2-D elastic with two different masses: (x-U*v1)^2 + y^2 = (Uv1)^2 (example, two billiard balls), the second mass is at rest. It's a equation which leads to a circle where all of the possible p2' lie on the circle. v1 is the velocity, x and y are the components of p2 vector (the momentum of the second object after collision ),and U= m1*m2/(m1+m2) is the reduced mass. 2. Conversation of momentum in 2-D: p1 (vector) = p1' (vector) + p2' (vector) with p2 = 0 (vector) Conversation of kinetic energy: p1^2/2m1 = p1'^2/2m1 + p2'^2/2m2 3. Attempt at solution Now I know how to get to this point: p1^2/(2m1) = (p1-x)+y^2/(2m1) + (x^2+y^2)/m2 (1) What I did, was to put my center of my frame of reference into the second object. There I can you some geometry to get p1' (momentum of object 1 after collision) = (p1-x) + y^2 And p2' (momentum of object 2 after collision)= x^2+y^2 I put those 2 into my conversation of kinetic energy equation which leads me to (1) Now the problem I face is, that I don't know how to get from equation (1) to the equation from the beginning. I know it is simple algebra, but I've been trying now for 1,5 hour and can't get there. Other sources skip the step from (1) to the equation and just say it is like that. Big thanks in advance for help!