Cambridge Encyclopedia » Cambridge Encyclopedia Vol. 23

ellipse - Parameterisation, Eccentricity, Semi-latus rectum and polar coordinates, Area, Circumference, Stretching and projection

constant focus distance line

In mathematics, the locus of a point which moves so that the sum of its distances from two fixed points (or foci) is constant. It can also be defined as a section of a double cone, or as the locus of a point which moves so that the distance from the focus is proportional to its distance from a fixed line (the directrix), the constant of proportion being less than 1. The Cartesian equation of an ellipse can be put in the form x2/a2 + y2/b2 = 1. The polar equation of an ellipse with the focus as pole and the major axis as base line is r = l/(1 + e cos ?). The planets move around the Sun in ellipses, and the shape is much used in art and architecture.

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