Multivariable Calculus - Level Curves

Question

Question: Show that $x^2+y^2=6$ is a level curve of $f(x,y)=\sqrt{x^2+y^2} -x^2-y^2+2$.

Not sure how to approach this...can anyone help?

Answer 1

Simply note that for $x^2+y^2=6$

$$f(x,y)=\sqrt{x^2+y^2} -x^2-y^2+2=\sqrt 6-6+2=\sqrt 6-4=\text{constant}$$