# Hyperbole

Hyperbole is a set of points in the plane, where the difference of the distances of the points from two fixed points is constant. The two points are called focal points..

$${r}_{2}-{r}_{1}=2a=const$$

$$e=\sqrt{{a}^{2}+{b}^{2}}$$

## Equation of hyperbole

$$\frac{(x-u{)}^{2}}{{a}^{2}}-\frac{(y-v{)}^{2}}{{b}^{2}}=1$$

## Central Hyperbole

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

## Tangency condition of a central hyperbole and a line

$${a}^{2}\xb7{k}^{2}-{b}^{2}={n}^{2}$$

where the equation of the tangent line is :

$$y=kx+n$$

Keywords: hyperbole, central hyperbole, Tangency condition of a central hyperbole and a line