Linked from
The 10 pages that link to Hyperbola, each with the reason it gives.
CircleCompared with: It is an open conic, unlike the closed circle.
Conic sectionBroader topic: A plane cutting both nappes produces two branches.
ParabolaCompared with: A hyperbola has eccentricity above one and two branches, unlike a parabola.
ConeBroader topic: A plane intersecting both halves of a double cone produces this section.