MAT201 quadric surfaces

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6 Terms

1
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ellipsoid

x²/a² + y²/b² +z²/c² = 1

-3 positive squared terms

-ellipse traces circle a, b, and c

-if a = b = c, sphere!

-if a = b or b = c or a = c, ellipsoid of revolution

2
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hyperbolic paraboloid

-x²/a² + y²/b² = z/c

condition: c > 0

-1 negative term * opens up on unsquared term


3
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elliptic hyperboloid of one sheet

x²/a² + y²/b² - z²/c² = 1

*opens on negative term

4
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elliptic hyperboloid of two sheets

-x²/a² - y²/b² + z²/c² = 1

*opens onto the positive term

5
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elliptic paraboloid

x²/a² + y²/b² = z/c

2 parabolas, 1 ellipse

opens onto nonsquared term

6
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elliptic cone

x²/a² + y²/b² = z²/c²

*double cone, single cone is the squared version

*opens on negative term