Level Curves Problem Show that $x^2+y^2=6$ is a level curve of $f(x,y)=\sqrt{x^2+y^2}-x^2-y^2+2$.
I know that the first equation is a circle but I do not know how to find out if the second one is it too.
Thanks for the help.
(Sorry my English is not good).

With
$x^2 + y^2 = c, \; \text{ a constant}, \tag 1$
for any $c$, we have
$f(x, y) = \sqrt{x^2 + y^2} - x^2 - y^2 + 2 =  \sqrt{x^2 + y^2} - (x^2 +  y^2) + 2 = \sqrt c - c + 2; \tag 2$
thus the circle (1) lies in the $\sqrt c - c +2$-level set of $f(x, y)$; note we needn't prove 
$f(x, y) = c_0, \; \text{a constant} \tag 3$
describes a circle to establish this.
