No because you have minus xy, not minus constants ab, i.e.

x^2+y^2-xy/k=0 - Wolfram|Alpha

not

ellipse - Wolfram|Alpha

E.g. for k = 1/4

x^2+y^2-4xy=0 - Wolfram|Alpha

and k = 1/2

x^2+y^2-2xy=0 - Wolfram|Alpha

and k from -1/2 to 1/2

z= (xy)/(x^2 + y^2) - Wolfram|Alpha