327:(or over the algebraic closure of the field of the coefficients, in the case of conics over general fields) into two linear factors. This implies that circles of negative radius and ellipses without real points are not degenerate. As far as I know, only the definition of section "Discriminant" is widely accepted. It allow a definition of degeneracy that is independent of the field (the circle of radius 3 has no rational point, and, with the definition of the lead should be degenerate over the rational numbers). This mess must be corrected.
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The article states that imaginary circles, and, more generally imaginary ellipses are degenerate. Nevertheless, it is stated, in section "Discriminant" that a conic is degenerate if and only its discriminant is zero, which means that the equation of the conics may be factored over the complex numbers
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Is it not possible, inside
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infinity) or d) a circle. A degenerate parabola: a) one line or b) a pair of parallel lines. Only for the degenerate hyperbola there is a common sense.--
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What a bummer! The hyperbola and parabola pages have great pictures.
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nowhere on the circle page is it stated that radii are nonzero.
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