Quadric Surfaces

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Last updated 12:18 AM on 9/4/26
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6 Terms

1
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Ellipsoid

x² + y² + kz² = 1

+++

2
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Hyperboloid One Sheet

x² +y² - z² =1

++- => odd one out (negative term) determines along axis

3
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Hyperboloid Two Sheets

x² - y² - z² = 1

+— => odd one out (positive term) determines along axis


4
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Double Cone

z² = x² + y² or x² + y² - z² = 0

no c term

if square root, only half cone

5
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Elliptic Paraboloid

z = x² + y² or x² + y² - z = 0

one term is 1st degree

++-

odd one out determines along axis

6
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Hyperbolic Paraboloid

z = x² - y² or x² - y² - z = 0

one term is 1st degree

+—

odd one out determines along axis