Yes, that's also what happens in the relation of the "Poincare half- plane model" for hyperbolic geometry to the "Poincare disk model"- a line in the plane model is equivalent to a circle (through the center of the disk) in the Poincare disk model. I'm not sure what you mean by "If it has an end point at infinity". It is possible for aray, not a line, to have one end point at infinity, and one at a "finite" point. Is that what you meant?