Conic section

In mathematics, a conic section (or just conic) is a curved locus of points, formed by intersecting a cone with a plane. The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their properties.

Semi-latus rectum and polar coordinates

The semi-latus rectum of a conic section, usually denoted l, is the distance from the single focus, or one of the two foci, to the conic section itself, measured along a line perpendicular to the major axis. It is related to a and b by the formula al=b^2,!, or l=a(1-e^2),!.

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In polar coordinates, a conic section with one focus at the origin and, if any, the other on the positive x-axis, is given by the equation

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: r (1 - e cos heta) = l,!.

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