A hyperbola is a curve that is the locus of all points in the plane such that for any point $P$ of the set, the absolute difference of the distances $\left|PF_1\right|$, $\left|PF_2\right|$ to two fixed points $F_1$, $F_2$ (called the foci) is constant, usually denoted by $2a$, $a>0$.

The midpoint of the line segment joining the foci is called the center/centre of the hyperbola.

The distance $c$ of the foci to the center/centre is called the focal distance or linear eccentricity. The eccentricity of the hyperbola is given by $e=\frac{c}{a}$.

The equation of a hyperbola with vertex $\left(x_0,\,y_0\right)$ in Cartesian coordinates is

The parametric equations of a hyperbola with vertex $\left(x_0,\,y_0\right)$ can be given by

In polar coordinates, the equation of a hyperbola with parameter $a$ and center/centre $\left(0,\, 0\right)$ is given by