Level curve of the function $f(x,y)=\min\{x^2+y^2,xy\}$

Question

How I can find the level curve of the function $$f(x,y)=\min\{x^2+y^2,xy\}$$

From where I need to start to solve this problem?

Thank you!

Answer 1

Hint: If $xy \geq 0$ then $x^2+y^2 \geq 2xy \geq xy$. If $xy <0$ then $x^2+y^2>xy$. Therefore, $f(x,y)=xy.$