Pair of Tangents

Pair of Tangents

For:

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

define:

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

For an external point $$P(x_1,y_1)$$:

$$S_1=\frac{x_1^2}{a^2}-\frac{y_1^2}{b^2}-1$$

and:

$$T=\frac{xx_1}{a^2}-\frac{yy_1}{b^2}-1$$

The pair of tangents is:

$$T^2=SS_1$$

Usage

- Used to obtain the combined equation of the two tangents from a point.