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The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations is called Analytic Geometry. Analytic geometry is also called coordinate geometry since the objects are described as n-tuples of points (where n=2 in the plane and 3 in space) in some coordinate system.Conic sections are the curves which can be derived from taking slices of a “double-napped” cone. (A double-napped cone, in regular English, is two cones “nose to nose”, with the one cone balanced perfectly on the other.) “Section” here is used in a sense similar to that in medicine or science, where a sample (from a biopsy, for instance) is frozen or suffused with a hardening resin, and then extremely thin slices (“sections”) are shaved off for viewing under a microscope. If you think of the double-napped cones as being hollow, the curves we refer to as conic sections are what results when you section the cones at various angles

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