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Let $S$ be an ellipsoid centered at the origin whose semiaxes are of length $1/2$, $1/2$ and $1/3$.

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

$\frac{r^2}{4}+9z^2=1$

$\frac{r^2}{4}+\frac{z^2}{9}=1$

$r^2+9z^2=1$

$4r^2+9z^2=1$

$r^2+\frac{z^2}{9}=1$