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Unformatted text preview: yaxis. It matches with III. 26. This is a cone with elliptical cross sections and the yaxis for its axis; it matches with I. 28. This is a hyperbolic paraboloid. The only one graphed is V. 33. We complete the square: 4 x 2 + ( y2) 2 + 4( z3) 2 =36 + 4 + 36 = 4 . We then get x 2 + ( y2) 2 2 2 + ( z3) 2 = 1 . This is an ellipsoid whose center is at (0 , 2 , 3) .42 y 2 442 x 2 442 z 2 4 45. This is very similar to the focusdirectrix deFnition of a parabola, so I’m thinking it’s probably a paraboloid. Let’s check it out. The square of the distance from the generic point ( x, y, z ) to the point (1 , , 0) is ( x + 1) 2 + y 2 + z 2 . The square of the distance from ( x, y, z ) to the plane x = 1 is ( x1) 2 . These two quantities are supposed to be equal. We get x 2 + 2 x + 1 + y 2 + z 2 = x 22 x + 1 , so4 x = y 2 + z 2 . This is indeed a circular paraboloid....
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This note was uploaded on 04/07/2008 for the course MTH 249 taught by Professor Starr during the Spring '08 term at Willamette.
 Spring '08
 Starr

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