Generalized circle question

Hi guys,

Generalized circle aka circle in the extended complex plane.

If such creature passes through the point at infinity, is it always a line when projected down to the complex plane?

If it has an end point at infinity, is it still a line?

I'm not really looking for proof, just something to base my intuition on. Thanks.

Re: Generalized circle question

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 a **ray**, not a line, to have one end point at infinity, and one at a "finite" point. Is that what you meant?