Parametric Coordinates Using Hyperbolic Functions

Parametric Coordinates Using Hyperbolic Functions

A point on:

$$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

can also be represented as:

$$P(a\cosh t,b\sinh t)$$

using:

$$\cosh^2t-\sinh^2t=1$$

Terminology

- $$t$$ → Hyperbolic parameter.

- $$\cosh t$$ → Hyperbolic cosine.

- $$\sinh t$$ → Hyperbolic sine.

Usage

- Useful for advanced parameter-based problems involving hyperbolas.