Conic section

In mathematics, a conic section (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with aplane. In analytic geometry, a conic may be defined as a plane algebraic curveof degree 2. There are a number of other geometric definitions possible. One of the most useful, in that it involves only the plane, is that a conic consists of those points whose distances to some point, called a focus, and some line, called a directrix, are in a fixed ratio, called the eccentricity.

Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it is sometimes called the fourth type of conic section. The type of a conic corresponds to its eccentricity, those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas. In the focus-directrix definition of a conic the circle is a limiting case with eccentricity 0. In modern geometry certain degenerate cases, such as the union of two lines, are included as conics as well.

The conic sections were named and studied at least since 200 BC, when Apollonius of Perga undertook a systematic study of their properties.

Latus Rectum is the line through the focus and parallel to the directrix.

The length of the Latus Rectum is 2b²/a.