Quadric Equations

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11 Terms

1
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Ellipsoid Equation

all signs are positive

<p>all signs are positive</p>
2
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How to obtain traces

Traces are obtained by intersecting the surface with planes parallel to one of the coordinate planes

3
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Hyperboloid of One Sheet

When x, y, and z are on the same side of the equation, two terms have a positive sign, one has a negative sign

<p>When x, y, and z are on the same side of the equation, two terms have a positive sign, one has a negative sign</p>
4
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Hyperboloid of Two Sheets

When x, y, and z are on the same side of the equation, two terms have a negative sign, one has a positive sign

<p>When x, y, and z are on the same side of the equation, two terms have a negative sign, one has a positive sign</p>
5
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Elliptic Cone

(x/a)² + (y/b)² = (z/c)²

<p>(x/a)² + (y/b)² = (z/c)²</p>
6
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Elliptic Paraboloid

both non-z terms are positive

<p>both non-z terms are positive</p>
7
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Hyperbolic paraboloid

z = (x/a)² - (y/b)²

<p>z = (x/a)² - (y/b)²</p>
8
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Right circular cylinder of radius r

x² + y² = r²

9
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Elliptic cylinder

(x/a)² + (y/b)² = 1

10
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Hyperbolic cylinder

(x/a)² - (y/b)² = 1

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Parabolic Cylinder

y = ax²