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\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1
Ellipsoid
\frac{x^2}{a^2}+\frac{y^2}{b^2}=\frac{z^2}{c^2}
Cone
\frac{x^2}{a^2}+\frac{y^2}{b^2}=\frac{z}{c}
Elliptic Paraboloid
\frac{x^2}{a^2}-\frac{y^2}{b^2}=\frac{z}{c}
Hyperbolic Paraboloid
\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1
Hyperboloid of One Sheet
-\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1
Hyperboloid of Two Sheet

Ellipsoid

Cone

Elliptic Paraboloid

Hyperboloid of one sheet

Hyperboloid of two sheets

Hyperbolic paraboloid