Belonging to the hyperbola; having the nature of the hyperbola. [1913 Webster]
Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression. Fuller. [1913 Webster]

Hyperbolic functions (Math.), certain functions which have relations to the hyperbola corresponding to those which sines, cosines, tangents, etc., have to the circle; and hence, called hyperbolic sines, hyperbolic cosines, etc. -- Hyperbolic logarithm. See Logarithm. -- Hyperbolic spiral (Math.), a spiral curve, the law of which is, that the distance from the pole to the generating point varies inversely as the angle swept over by the radius vector.

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OXFORD DICTIONARY

hyperbolic, adj. Geom. of or relating to a hyperbola.

Idiom

hyperbolic function a function related to a rectangular hyperbola, e.g. a hyperbolic cosine.

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