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Suppose we have a sphere with radius $3$ centered at $(-3,3,2)$. What is the equation of the trace of this sphere on the $xy$ plane?

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    Write down the equation of the sphere. Intersect it with $xy$ by substituting $z = 0$. You'll get a circle of center $(-3, 3, 0)$ and radius $\sqrt{5}$. The projection of the sphere is concentric but has bigger radius: $3$.2012-08-29

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