Equation of Catenary/Formulation 1

Curve
Consider a catenary.

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

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

where $a$ is a constant.

The lowest point of the catenary is at $\tuple {0, \dfrac 1 a}$.