Parametric Coordinates of a Hyperbola

Parametric Coordinates of a Hyperbola

For:

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

a point on the hyperbola can be represented as:

$$P(a\sec\theta,b\tan\theta)$$

using:

$$\sec^2\theta-\tan^2\theta=1$$

Terminology

- $$\theta$$ → Parametric angle.

Usage

- Used to represent points on a hyperbola and simplify tangent, normal and chord calculations.

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