Not really for homework help, but just for curiousity. Is there a way to distinguish whether the graph is a parabola or a hyperbola if you do not know the equations and one side of the hyperbola is missing (so there's just one U shape) by restricting the domains or ranges.

Question

I know that hyperbola generally is more ellipitical, is that the answer? I am just wondering if a parabola can be just as elliptical depend on how fast it grows.

Answer 1

A hyperbola has asymptotes, that is, there is a pair of lines which a hyperbola approaches but never actually reaches.

A parabola has no such property.