Find the coordinates of center of the sphere $x^{2} + y^{2} + z^{2} - 3 x - 2 y + 2 z - 15 = 0$

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Solution

The equation is of the form $x^{2} + y^{2} + z^{2} + 2 g x + 2 f y + 2 h z + c = 0$
Comparing the above equation we get
$2 g = - 3 \Rightarrow g = \frac{- 3}{2}$
$2 f = - 2 \Rightarrow f = - 1$
centre: $(\frac{3}{2}, 1, - 1)$

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