When finding the center of a sphere, you will be given an equation of a sphere. And all you have to do is complete the square essentially..but three times. For instance...
x^2 + y^2 - 2x + z^2 - 4z + 10y - 4 = 0
First you should combine the terms
x^2 - 2x + _ + y^2 + 10y + _ + z^2 - 4z + _ = 4
Now complete the square three times!
(x^2 - 2x + 1) + (y^2 + 10y + 25) + (z^2 - 4z + 4) = 4 + 1 + 25 + 4
Factor
(x - 1)^2 + + 5)^2 + - 2)^2 = 34
Pull out terms!
center: (1, -5, 2)
radius: √34
YAY
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