In the monofocal (involving only one focus) definition of conic sections, the focus is the point associated with a line (called the directrix) so that the conic section is defined as the locus of points for each of which the distances to the focus divided by the distances to the directrix is a constant. The constant is called the eccentricity of the conic section.
Therefore, we obtain the relation d(P, F) = e d(P, H), where e is the eccentricity of the conic section. The value of e, which is a strictly positive real number, determines whether the conic section is an ellipse, a parabola or a hyperbola.
In the bifocal definition of a conic section (ellipse or hyperbola, which have two foci), these figures are defined as a function of the sum or difference of the distances from their points to each of the foci.