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Why are certain PDE called "elliptic", "hyperbolic", or "parabolic"?

Why are the Partial Differential Equations are so named? i.e, elliptical, hyperbolic, and parabolic. I do know the condition at which a general second order partial differential equation becomes these, but I don't understand they are so named?

Does it have anything to do with the ellipse, hyperbolas and parabolas?



from Hot Weekly Questions - Mathematics Stack Exchange

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