A hyperbola is the locus of a point in a plane which moves in the plane in such a way that the ratio of its distance from a fixed point (called focus) in the same plane to its distance from a fixed line (called directrix) is always constant which is always greater than unity.
The constant ratio is generally denoted by ‘e’ and is known as the eccentricity of the hyperbola.
Every hyperbola has a second focus and second directrix.
The difference of the focal distances of any point on a hyperbola is constant and is equal to the length of transverse axis of the hyperbola.
A second definition of the hyperbola
On account of this property, a second definition of the hyperbola is:
A hyperbola is the locus of a point which moves in such a way that the difference of its distance from two fixed points (foci) is always constant.