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Unformatted text preview: Surfaces in Space  (10.6) 1. Cylindrical Surfaces The equation ! x ! h " 2 ! ! y ! k " 2 " r 2 is a circle with center ! h , k " and radius r in the xy ! plane. In the xyz ! space, the equation ! x ! h " 2 ! ! y ! k " 2 " r 2 means ! x ! h " 2 ! ! y ! k " 2 " r 2 !" # z # " , or ! x ! h " 2 ! ! y ! k " 2 " r 2 a # z # b and its graph is a cylinder which is perpendicular to the xy ! plane. The intersection of the surface and the plane z " c ( a # c # b " is a circle: ! x ! h " 2 ! ! y ! k " 2 " r 2 , which is called t he trace of the surface in the plane z " c .21 1 242 2 4 t2 2 z ! x ! 1 " 2 ! ! y ! 2 " 2 " 4 ! 2 # z # 24 242 4 y2 t & ! x ! 1 " 2 ! ! y ! 2 " 2 " 4, z " 1.. ! x ! 1 " 2 ! ! y ! 2 " 2 " 4, z " ! 2 Similarly, graphs of equations ! x ! h " 2 ! ! z ! l " 2 " r 2 , and ! y ! k " 2 ! ! z ! l " 2 " r 2 are cylinders perpendicular to the xz ! plane and the yz ! plane, respectively....
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This note was uploaded on 02/05/2012 for the course MATH 2142 taught by Professor Lerna during the Fall '10 term at FIU.
 Fall '10
 Lerna

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