# Catenary Curve

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Catenary curve has a u-shaped curve and can be represented by a hanging chain or cable under its own weight and supported only at it's ends.

### Catenary Curve formula

$$\large{ y = \frac{a}{2} \; \left( ^a\sqrt{e^x} \;+\; \frac{1}{^a\sqrt{e^x} } \right) }$$

Where:

$$\large{ y }$$ = y-coordinate (dimensionless)

$$\large{ a }$$ = parameter (dimensionless)

$$\large{ e }$$ = 2.71828182845904523536 ...

$$\large{ x }$$ = x-coordinate (dimensionless)