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degenerate conic
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conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve
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The discriminant test can be applied to degenerate conics.
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A pair of straight lines is called a degenerate conic.
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Table 8.2 displays the three basic types of conic sections grouped with their associated degenerate conics.
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The conic section defined by (19) is called a degenerate conic section.
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Each conic or degenerate conic is shown with a sample equation and the sign of its discriminant.
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These cases are called degenerate conics.
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Degenerate Conics Graph all of the degenerate conics listed in Table 8.2.
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These are usually called degenerate conics.
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Also note that if c a, then b 0, and we have a degenerate conic—that is, a point.
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If d/k1<0, then we have x'2<0 (which is impossible) and we obtain a degenerate conic.
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This paper presents the method to obtain, in Cartesian coordinates, the parallel curve lines of non-degenerate conical curves, by analytical and numerical methods.
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Each of the following represents a degenerate or imaginary conic.
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Degenerate cases of the conic sections are a point. a line, a pair of lines, or the empty set.
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The remaining conics are called degenerate and include single points and pairs of lines (see Exercise 15).
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The converse is also true: the Braikenridge–Maclaurin theorem states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line, then the six vertices of the hexagon lie on a conic, which may be degenerate as in Pappus's hexagon theorem.
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