Product of Distances from the Asymptotes

Product of Distances from the Asymptotes

For a point $$P(x,y)$$ on:

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

the product of its perpendicular distances from the two asymptotes is constant:

$$d_1d_2=\frac{a^2b^2}{a^2+b^2}$$

Usage

- Used in locus and distance problems involving the asymptotes.