Write the given equation in the form of an equation of a sphere and find its center and radius. x2 + y2 + z2 = 12x + 2y
equation =

center (x, y, z) =

radius =

Complete whatever squares you can:

x² - 12x = x² - 12x + 36 - 36 = (x - 6)² - 36

y² - 2y = y² - 2y + 1 - 1 = (y - 1)² - 1

So rewrite the equation as

x² + y² + z² = 12x + 2y

→   x² - 12x + y² - 2y + z² = 0

→   (x - 6)² - 36 + (y - 1)² - 1 + z² = 0

→   (x - 6)² + (y - 1)² + z² = 37

Then the center is (x, y, z) = (6, 1, 0), and its radius is √(37).

The radius is the square root of the constant term, z

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