Equation of Catenary/Formulation 1

Curve
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:
 * $y = \dfrac {e^{ax} + e^{-ax}} {2 a} = \dfrac {\cosh a x} a$

where $a$ is a constant.

The lowest point of the catenary is at $\left({0, \dfrac 1 a}\right)$.