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Ellipsoid
X²/a²+y²/b²=z²/c²
Hyperboloid of one sheet
X²/a²+y²/b²-z²/c²=1
Hyperboloid of 2 sheets
X²/a²-y²/b²-z²/c²=1
Cone
X²/a²+y²/b²-z²/c²=0
Elliptic paraboloid
Z/c=x²/a²+y²/b²
Hyperbolic parabaloid
Z/c=y²b²-x^/a²