Talk:Degenerate conic
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points are circles
editnowhere on the circle page is it stated that radii are nonzero.Grabba (talk) 19:37, 4 March 2010 (UTC)
- they're ellipses too. (but you knew that already) Grabba (talk) 19:39, 4 March 2010 (UTC)
No Pictures!
editWhat a bummer! The hyperbola and parabola pages have great pictures. — Preceding unsigned comment added by 24.99.55.149 (talk) 00:38, 5 June 2011 (UTC)
- Done. Loraof (talk) 21:06, 10 March 2017 (UTC)
Standard form for the equation of a conic section
editIs it not possible, inside Wikipedia, to agree about a standard form for the equation of a conic section? In each of the following articles the form used for the equation of a conic section is different.
http://en.wikipedia.org/wiki/Conic_sections#Cartesian_coordinates
http://en.wikipedia.org/wiki/Pole_and_polar#General_conic_sections
The article contradicts itself
editThe 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 (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. D.Lazard (talk) 10:58, 7 January 2016 (UTC)
degenerate ellipse,- parabola, - hyperbola
editOne should be more reluctant in using the terms degenerate ellipse, ..., because in literature there is no common use. A degenerate ellipse may be a) a point or b) a line segment or c) a parabola (one focus -> 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.--Ag2gaeh (talk) 09:46, 11 March 2017 (UTC)