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The Five Point Conic Section: Exploration with Computer Software

John H. Mathews
Organization: California State University Fullerton
Department: Mathematics
Journal / Anthology


It is well known that five points in the plane determine a conic section: ellipse, hyperbola, parabola, circle or the degenerate cases of two intersecting lines or two parallel lines. A quadratic euation in two variables defines the conic section implicitly.... At least one of the coefficients [of the equation] must be non-zero. If it is known a priori which coefficient c_j is nonzero, then each term can be divided by c_j to reduce the number of unknown coefficients to five. Hence five points uniquely determine a conic.

*Mathematics > Geometry > Plane Geometry