pu6l4-conic-sections-hyperbola

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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 a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of 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.- source wikipedia

Tagged under: conics,curve,intersection,conical,analytic,geometry,coordinates,plane,focus,directrix,eccentricity,fixed,ratio,hyperbola,parabola,ellipse,special,case,apollonius,perga,degenerate,asymptote,axis,vertex,symmetry,center,distance,formula,pythagorean,theorem,transverse,congjugate,inertia,slope,imaginary,diagonal,form,standard,general,completing,square,tip,axes,paraboloid,euclidean,arms,branches,major,minor,semi-major,semiminor,perpendicular,bisector,mirror

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