lect10_6

lect10_6 - Surfaces in Space - (10.6) 1. Cylindrical...

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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 .-2-1 1 2-4-2 2 4 t-2 2 z ! x ! 1 " 2 ! ! y ! 2 " 2 " 4 ! 2 # z # 2-4 2-4-2 4 y-2 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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lect10_6 - Surfaces in Space - (10.6) 1. Cylindrical...

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