ELLIPSE (Lat. ellipsis, from Gk. Mettptc, elleipsis, omission, from aReizeiv, elleipein, to omit, from iv, en, in + leipein, to leave). An important geometric figure, repre senting the approximate shape of the planetary orbits. It is one of the conic sections (q.v.) and received its name from Apollonius (q.v.). It is a curve of the second order and second class CravEs), and may be defined as the locus of a point (P), the sum of whose distances from two fixed points is constant. The two fixed points are called the foci (F and F') : the diameter drawn through them is called the major axis, and the perpendicular bisector of this diameter the minor axis. It is also defined as the locus of a point which moves so that the ratio of its dis tance from a fixed point, called the focus, to its distance from a fixed line (DIY), called the directrix, is constant and less than unity; the constant ratio is called the eccentricity of the ellipse and is equal to the ratio of the distance between the foci to the major axis. The limit of the ellipse, as the eccentricity approaches 0 and the foci approach coincidence, is the circle. There are various contrivances for describing an el lipse. called ellipsographs, or elliptic compasses.
The simplest method is to fix the two ends of a thread to pins at the foci. and make a pencil move in the plane. keeping the thread taut. The end of the pencil will trace an el lipse, whose major axis is equal to the length of the thread. The Cartesian equation of the el lipse placed symmetrically with respect to the x axis of coordinates (q.v.) is = 1, a, b being the semi-major and semi-minor axes re spectively. The eccentricity is bThe a polar equation of the ellipse is r 1 +ceose, where the parameter 1' . The centre 0 a bisects all chords: each diameter of a pair of conjugate (q.v.) diameters bisects all chords parallel to the other; and the focal chord paral lel to the directrix is called the loins rretum. from the equation of the ellipse, by means of the integral calculus, its area is shown to be rah. The length of its circumference is 1 - approxi- tely 27r,-/ 1 1 ( 2.e; 2.) There are s( veral special kinds of ellipses, for the name, and equations of which consult Jiro .ard, .\ofs dr filidioyoiphir des courbes fp'ome trIques I Itar 1897).