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12.6 CYLINDERS and QUADRATIC

SURFACES

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Cylinders A surface that is generated by moving a straight line along a given plane curve while holding the line parallel to a given fixed line.

The curve is called generating curve for the cylinder.

Example of a cylinder

Example: 1

The Parabolic Cylinder .Other Examples: elliptic cylinder, hyperbolic cylinder

Quadric Surfaces

Three dimensional analogues of ellipses, parabolas and hyperbolas.

Most general form of quadric surface is

Quadric surfaces are ellipsoids, paraboloids, elliptic cones and hyperboloids.

Example: 2 The ellipsoid

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Example: 3 The elliptic paraboloid

Ex:

Example: 4 The elliptic cone

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Example: 5 The hyperboloid of one sheet

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Example: 6 The hyperboloid of two sheets

, Ex:

Example: 7 The hyperbolic paraboloid

, Ex:

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