Pair of Tangents from an External Point

Pair of Tangents from an External Point

For:

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

define:

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

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

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

The pair of tangents from $$P(x_1,y_1)$$ is:

$$T^2=SS_1$$

Usage

- Used when the combined equation of the two tangents from an external point is required.