From a point on the hyperbola x2a2 − y2b2 = 1 lines are drawn to focus S
and directrix perpendicular to it as shown.Then,
A hyperbola by definition is the locus of a point in a plane which moves in the plne in such a way that the ratio of its distance from a fixed point, focus, in the same plane to its distance from a fixed line, called directrix, is a constant. This constant is always greater than 1, and is called eccentricity-, 'e'
i.e.,e = PSPD > 1
i.e.,PS > PD.