Let $(x,y)\in[0,1)\times[0,1)$ cum $x^2+y^2<1$. Are there any $\mu\geq\lambda>0$ such that
$$\lambda\xi_1^2+\lambda\xi_2^2\leq(1-x^2)\xi_1^2+2xy\xi_1\xi_2+(1-y^2)\xi_2^2\leq\mu\xi_1^2+\mu\xi_2^2$$
$\forall\xi=(\xi_1,\xi_2)^T\in\mathbb R^2$ ?
Let $(x,y)\in[0,1)\times[0,1)$ cum $x^2+y^2<1$. Are there any $\mu\geq\lambda>0$ such that
$$\lambda\xi_1^2+\lambda\xi_2^2\leq(1-x^2)\xi_1^2+2xy\xi_1\xi_2+(1-y^2)\xi_2^2\leq\mu\xi_1^2+\mu\xi_2^2$$
$\forall\xi=(\xi_1,\xi_2)^T\in\mathbb R^2$ ?