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\[f(x,y)=\sqrt{ln(\frac{9}{x^{2}+y^{2}})}\]

Somehow I find some technical difficulty with it.

I have found 3 conditions:

\[\ln \left ( \frac{9}{x^{2}-y^{2}} \right )\geq 0\]

**and**

\[\frac{9}{x^2-y^2}>0\]

**and**

\[x^2\neq y^2\]

This led me to understand that maybe an hyperbola is concerned, or a part of it anyway.

I understand that in order to keep

\[\ln \left ( \frac{9}{x^{2}-y^{2}} \right )\geq 0\]

I get

\[\frac{9}{x^2-y^2}\geq 1\]

after applying e. But I am kind of stuck now.

Your help will be most appreciated. I want to draw the domain at the end.