Sure, let's simplify it:
Your formulas are a type of 3D to 2D perspective projection. However, it's more common to divide by Z alone, not the sum of focal distance and Z:
PosX2D = (FocalDistance * PosX3D) / PosZ3D; PosY2D = (FocalDistance * PosY3D) / PosZ3D;
This provides a "camera" view, with objects appearing smaller the further they are. Note, this won't handle viewport transformations, and objects at Z=0 or negative Z may cause issues.