Question

Given f(x,y)=e^{-(x^2+y^2)}How do I find an equation for the contour where \[f(x,y)=e^{-2}\]

is it just

Answer 1

\[e^{-(x^2+y^2)}=e^{-2}\] ?

Answer 2

Is this right, or do I need more work? Any calculus gurus know?

Answer 3

This is right, so the equation is x²+y²=2 , a circle with radius sqrt(2).

Answer 4

So if you cut through the graph at height z= e^{−2}, you get that circle.