Is there a detailed list of conic sections, with their parametrization, Implicit function, first and second fundamental form?
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You might want to check out this document titled "Conic Sections Beyond $\mathbb{R}^2$". – Jose Arnaldo Bebita Dris Jul 24 '17 at 10:27
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the wikipedia article seems to be already quite complete, isn't it? – Surb Sep 11 '17 at 18:43
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Maybe helpful MSE reference: Confusion with the various forms of the equation of second degree . – Han de Bruijn Sep 12 '17 at 18:57
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First and second fundamental forms are entities associated with a surface in 3-space whereas the term conic section usually refers to a curve. A fairly detailed treatment of ellipses, hyperbolas, parabolas as well as discussion of degenerate cases can be found in my class notes for differential geometry here (see sections 2.6, 2.7 and following there).
Mikhail Katz
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