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\textbf{Partial Differentiation}

\textit{\textbf{Functions of more than one variable}}
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\textbf{Question}

Assume $z \ge 0$.

Given that $4z^2 = (x-z)^2 +(y-z)^2$ defines $z$ as a function of $x$
and $y$, sketch level curves of this function and describe its graph.


\textbf{Answer}

If $z=c>0$, we have $(x-c)^2+(y-c)^2=4c^2$ which is a circle in the
plane $z=c$, with centre $(c,c,c)$ and radius $2c$.

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