Hyperbola
The hyperbola is the intersection of double napped cone with plane parallel to the axis. The hyperbola is the locus of a point in a plane which moves so that its distance from a fixed point bears a constant ratio e (e > 1) to its distance from a fixed line . The fixed point is called the focus S and the fixed line is called the directrix d . If S is the focus and d is the directrix not containing the focus and P is the moving point, then PS/PM = e , where PM is the perpendicular on thr directrix . e > 1 called eccentricity of the hyperbola Standard Eqaution of The Hyperbola : Let S be the focus, d be the directrix and e be the eccentricity of a hyperbola . Draw SZ perpendicular to directrix . Let A and A ' divide the segment SZ internally and externally in the ratio e:1. By definition of hyperbola A and A ' lie on hyperbola. Let AA ' = 2a , midpoint O of segment AA' be the origine . Then O ≡ (0, 0) , A≡ (a, 0) and A ' ≡