A hyperbola is the set of all points in the plane, the difference of whose distance from two fixed distinct points is a given positive constant that is less than the distance between the fixed points.
In this definition the “difference” of the distances is understood to mean the distance to the farther point minus the distance to the closer point.
It can also be defined as the locus of a point in a plane whose distance from a fixed point bears a constant ratio to its distance from a fixed line. The fixed point is called the focus, the fixed line is called the directrix, and the constant ratio is called the eccentricity. The eccentricity of the hyperbola is denoted by and it is always greater than one. The hyperbola has two foci and two directrices.