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# 12.6 Cylinders and Quadric Surfaces - Math 224 Calculus III...

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Math 224 Calculus III 1 12.6 Cylinders and Quadric Surfaces Recommended Homework: #1-35. In 12.5 we considered lines and planes in 3 . Here we look at more complicated surfaces. Cylinders in Space Here a cylinder is not just the familiar right-circular cylinder, but any surface that is made up of all parallel lines (called rulings ) that are perpendicular to some 2D curve ( plane curve). This plane curve is a cross-section of the general cylinder. Example: A right-circular cylinder is the set of all parallel lines that are perpendicular to the cross- sectional (2D) curve; a circle: In general, the plane curve need not be circular. A cylinder is obtained when one of the variables is missing from the equation in 3 Example: Describe and sketch the surfaces 2 4 x y 2 2 9 16 y z

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Math 224 Calculus III 2 Quadric Surfaces General Form of a Quadric Surface: 2 2 2 0 Ax By Cz Dxy Exz Fyz Gx Hy Iz J To understand/describe quadric surfaces, we use traces. These are simply cross-sections of the surface taken with a selection of planes that are parallel to the

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12.6 Cylinders and Quadric Surfaces - Math 224 Calculus III...

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