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Find the center and radius of  the sphere for x^2 + y^2 + z^2 - 4x + 8y + 6z + 4 = 0

 Sep 3, 2020
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"complete the square' for    x   y  and z

x^2-4x               +       y^2+8y         +   z^2 +6z          =  4

(x-2)^2             +         (y+4)^2        +   (z+3)^2           = 4   + 4   + 16    + 9

 

center is thus     2, -4, -3           radius = sqrt (4+4+16+9) = sqrt 33  

 Sep 3, 2020

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