Like you correctly said, the short-period comets are thought to originate in the Kuiper Belt, which is an area outside Neptune's orbit, which is located from thirty to fifty light-year.
Comets with shorter orbital periods are located in “Kuiper Belt”.
<u>Explanation:</u>
Short comets are orbiting the Sun in the exact surface as the planets encircle the sun, because they are discovered closer to the ecliptic. Those short orbital comets is discovered in ''Kuiper Belt''. It can be also called as the ''Edgeworth''. The Kuiper Belt is a disk-shaped area beyond Neptune's orbit, rising from the outside and containing many objects similar to ice comets.
The cloud in inner solar system were created nearer to the sun than Kuiper Belt is called as ''Oort cloud''. The small objects were emitted from the solar system in clash with gravity that are nearer to the giant planets. Distant Oort cloud formed by those who could not escape completely. Small objects with further shapes had no such interaction and remained as objects in the Kuiper Belt.
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