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Ellipsoid (or sphere)
x²/a² + y²/b² + z²/c² = 1
Cylinder/circle
x²+y² = constant

Cone
x²/a² + y²/b² = z²/c²

Elliptic Paraboloid
x²/a² + y²/b² = z/c

Hyperboloid of One Sheet
x²/a² + y²/b² -z²/c² = 1

Hyperboloid of Two Sheets
-x²/a² - y²/b² + z²/c² = 1