13.6 Surfaces

13.6 Surfaces - ET 12.6; M 13.6. Surfaces Quadratic curves....

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Unformatted text preview: ET 12.6; M 13.6. Surfaces Quadratic curves. In R2 , some quadratic equations define curves. Cylinders. A cylinder in R3 is the set of all points in all lines that are parallel to a given line and meet a given curve. Some coordinate fails to appear in the equation of the cylinder when the given line is parallel to that coordinate axis. Basic quadric surfaces. Consider quadratic equations in three variables with no terms involving products of distinct variables. Completing squares and shifting reduces matters to just a few cases. The corresponding surfaces in R3 have traces in planes parallel to coordinate planes. The traces are standard two-dimensional quadratic graphs. They reveal the nature of the quadric surface. The End 19 January 2007 ...
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This note was uploaded on 01/26/2011 for the course MATH 200 taught by Professor Unknown during the Spring '03 term at UBC.

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