Solution
= Solution
The denominator $D=x^2+xy+y^2=(x+y/2)^2+3y^2/4$ is positive away from the origin. The <partial derivatives> are
$$
f_x=\frac{y(y^2-x^2)}{D^2},\qquad f_y=\frac{x(x^2-y^2)}{D^2}.
$$
They both vanish exactly on
$$
\boxed{y=x\quad\text{and}\quad y=-x,\qquad(x,y)\ne(0,0).}
$$
These are lines of <stationary points>, with values $1/3$ and $-1$, respectively.