Which source for a comet

If the comet had just a tiny velocity, it would likely miss the sun and be in an elliptical orbit that comes close to the sun and then goes back out to where the comet started from, over and over again. So we could use the calculated orbit to figure out where the comet will be when it is furthest from the sun.

1. If very far from the sun and not near the plane of the ecliptic, it probably came from the Oort cloud.
2. If not so far from the sun and near the plane of the ecliptic, it probably came from the Kuiper belt.