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[tex]2x^2+y^2 = x^2-y^2\\\\ 2x^2 - x^2 + y^2 + y^2 = 0\\\\ x^2 + 2y^2=0\\\\ x^2 = 0~~~\Longrightarrow~~~\boxed{x=0}\\\\ 2y^2 = 0~~~\Longrightarrow~~~y^2 = 0~~~\Longrightarrow~~~\boxed{y=0}\\\\ [/tex]