Hyperbola

HYPERBOLA

Hyperbola is a curve traced out by a point moving in a plane such that the difference between its distances from two fixed points (called the foci), is a constant. A hyperbola has two branches, two foci and two directrices as shown in Fig. 6.20.

Sum of the distances of the point measured from two Foci ie., (F1P+ PF2) is known as length of Thread. It is also to be noted that (PF1 - PF2) = a constant, which is equal to the distance V1 - V2 ie., the distance between the vertices.

A single branch of hyperbola is defined as the locus of a point P moving in a plane such that the ratio of its distance from a fixed point, called focus to the fixed straight AAA RO MOTOUR line, called Directrix is a constant and is always greater than unity. 

Eccentricity, e = Distance of the point from Focus / Distance of the point from Directrix 

= a constant > 1

Refering the Fig. 6.21, e = FP/PM

For a single branch of hyperbola, definitions like Fig. 6.21 Focus, Directrix, Abscissa, Ordinate, Double ordinate, Latus to elsoa Rectum etc., are defined as explained for a parabola.