Equation of Catenary/Formulation 2

Theorem
Consider a catenary.

Let a cartesian coordinate plane be arranged so that the y-axis passes through the lowest point of the catenary.

The catenary is described by the equation:
 * $y = \dfrac a 2 \paren {e^{x / a} + e^{-x / a} } = a \cosh \dfrac x a$

where $a$ is a constant.

The lowest point of the chain is at $\tuple {0, a}$.