s10wk01 - so the terms x 2-6 x = ( x-3) 2-9 . Likewise, 2 y...

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Math 23, Spring 2010 B. Dodson J. Ortiz 1. Course Info 2. Week 1 Homework: 12.1: 3-Space, Distance Note: weekly slides (these) will be posted on blackboard. daily slides (larger font, more pages) may be found on http://www.lehigh.edu/ bad0/courses Problem 12.1.15: Show that the equation x 2 + y 2 + z 2 - 6 x + 4 y - 2 z = 11 represents a sphere, and find its center and radius. Solution: ( x - a ) 2 = x 2 - 2 ax + a 2 ,
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Unformatted text preview: so the terms x 2-6 x = ( x-3) 2-9 . Likewise, 2 y 2 + 4 y = . . . z 2-2 z = . . . y 2 + 4 y = ( y + 2) 2-4 z 2-2 z = ( z-1) 2-1, so x 2 + y 2 + z 2-6 x + 4 y-2 z = ( x-3) 2-9 + ( y + 2) 2-4 + ( z-1) 2-1 = 11 , or ( x-3) 2 + ( y + 2) 2 + ( z-1) 2 = 11 + 9 + 4 + 1 = 5 2 . conclusion: center = (3, -2, 1), radius = 5....
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s10wk01 - so the terms x 2-6 x = ( x-3) 2-9 . Likewise, 2 y...

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