x^2+y^2=(1/5)(x-2y)^2+(1/5)(2x+y)^2.
x^2+3y^2=(3/4)(x-y)^2+(1/4)(x+3y)^2.
x^2+3y^2=(3/7)(x-2y)^2+(1/7)(2x+3y)^2.