Unformatted text preview: Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 is a conic in the xyplane. Degenerate Forms of Conics Degenerate forms can be obtained from the above, and degenerate forms can be graphs of no points, one point, a line, a pair of intersecting lines, or a circle. Identifying Conics The conic given by the equation Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 can be identiﬁed by the value of its discriminant B 24 AC as follows: B 24 AC = 0 Parabola or degenerate form B 24 AC < 0 Ellipse or degenerate form B 24 AC > 0 Hyperbola or degenerate form The following illustrates how the various conics are obtained from the intersections of planes with a cone. 1...
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 Fall '11
 Kutter
 Algebra, Conic Sections, Conic section, xy −plane, Conics Degenerate forms

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