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notes001 (18) - x 2& 6 x 9 y 2 4 y 4 z 2& 2 z 1 = 11...

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August 24, 2009 NAME____________________________________________ Show that the equation x 2 + y 2 + z 2 6 x + 4 y 2 z = 11 Solution: The above equation can be written as x 2 6 x + y 2 + 4 y + z 2 2 z = 11 . By ±completing the squares²we obtain
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Unformatted text preview: x 2 & 6 x + 9 + y 2 + 4 y + 4 + z 2 & 2 z + 1 = 11 + 9 + 4 + 1 or ( x & 3) 2 + ( y + 2) 2 + ( z & 1) 2 = 25 . This shows that the equation represents a sphere with center at the point (3 ; & 2 ; 1) and radius 5 . 1...
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This note was uploaded on 02/05/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.

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