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Let $S$ be the surface whose equation in spherical coordinates is $\phi =\pi /4$.

What is the equation of $S$ in rectangular coordinates?

$x^2+y^2=z^2$

$x^2+y^2=2z^2$, $z\geq 0$

$x^2+y^2=z^2$, $z\geq 0$

$x^2-y^2=z^2$

$x^2+y^2=z^2+1$, $z\geq 0$