Consider the function

$f(x,y)=\frac{1}{\sqrt[\phantom{2}]{9-x^2-y^2}}$

The level curves $f(x,y)=k,k>0$ of $f$ are circles.

Select one:

a$.$ with the center at $(3,3)$ and the radius $3$

b$.$ with the center at $(0,0)$ and the radius

$\sqrt[\phantom{2}]{9-\frac{1}{k^2}},k>0$

c$.$ with the center at $(3,3)$ and the radius

$\sqrt[\phantom{2}]{9-\frac{1}{k^2}},k>0$

d$.$ with the center at $0,0)$ and the radius

$\sqrt[\phantom{2}]{?}9-k^2,k>0$

e$.$ none of these