Definition time:

..."therefore the shape of this curve (often called a "catenary curve") is
the graph of the hyperbolic cosine function. Hence we see graphs of
hyperbolic cosines every time we look at telephone or electric cables
suspended between poles."

from 'Calculus with Analytical Geometry by Daniel J. Fleming and James J.
Kaput (who tried to teach me DiffEQs) Department on Mathmatics University of
Massachussettes N. Dartmouth.

a possible answer to the original  question

tim

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