Question: For constants a, b, c, and d, show that the equation x 2 + y 2 + z 2 - 2ax - 2by - 2cz

For constants a, b, c, and d, show that the equation

x2 + y2 + z2 - 2ax - 2by - 2cz = d

describes a sphere centered at (a, b, c) with radius r, where r2 = d + a2 + b2 + c2, provided d + a2 + b2 + c2 > 0.

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