Quadriques

Classification des quadriques.

Quadriques non-dégénérées
Signature (3;0) Signature (2;1)
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\[ \frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=0 \]
Le point (0;0;0).
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\[ \frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=-1 \]
L'ensemble vide.
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Quadriques dégénérées

Signature (2;0) Signature (1;1) Signature (1;0)
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\[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=0 \]
La droite (Oz)
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\[ \frac{x^2}{a^2}+\frac{y^2}{b^2}=-1 \]
L'ensemble vide.
\[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=-1 \]
Cylindre hyperbolique.
\[ \frac{x^2}{a^2}=-1 \]
L'ensemble vide.