Parabola/Hyperbola

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.

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.

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  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.

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