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## Main Question or Discussion Point

I am trying to find the level curves for the function g(x,y)= k = xy/(x^2+y^2).

I get, x^2+y^2-xy/k=0.

I know this is an ellipse, but I do not know how to factor, and find values of k for which the level curves exist.

I get, x^2+y^2-xy/k=0.

I know this is an ellipse, but I do not know how to factor, and find values of k for which the level curves exist.