Question

What shape are the orbits of most comets?

Answer 1

Most comets orbit in very elongated ellipses, possibly going as far as a light year from the Sun
(https://en.wikipedia.org/wiki/Oort_cloud).

Explanation:

When something orbits in a highly elongated ellipse like most comets, it's close to escaping entirely if the object gains a little extra energy from the gravity of other bodies (maybe even a passing star).

Or, if the object loses instead of gains energy from the gravity of other bodies, it's easily pushed down to a more compact orbit. This might have happened to Halley's Comet (https://en.wikipedia.org/wiki/Halley%27s_Comet).