Find largest possible value of $x^2+y^2$ given that $x^2+y^2=2x-2y+2$ 
Let $x, y \in \mathbb R$ such that $x^2+y^2=2x-2y+2$.  Find the largest possible value of $x^2+y^2$.

My attempt:
$x^2+y^2=2x-2y+2$
$(x^2-2x)+(y^2+1)=2$
$(x-1)^2+(y+1)^2=4$
I have no idea how to continue here.  Any help?

We have the following quadratically constrained quadratic program (QCQP) in $\mathrm x \in \mathbb R^2$
$$\begin{array}{ll} \text{maximize} & \| \mathrm x \|_2^2\\ \text{subject to} & \| \mathrm x - \mathrm c \|_2^2 = 4\end{array}$$
where $\mathrm c \in \mathbb R^2$ is given. Let $\rm y := x-c$. Hence, we obtain the following QCQP in $\mathrm y \in \mathbb R^2$
$$\begin{array}{ll} \text{maximize} & \| \mathrm y + \mathrm c \|_2^2\\ \text{subject to} & \| \mathrm y \|_2^2 = 4\end{array}$$
Using the Cauchy-Schwarz inequality and $\| \mathrm y \|_2 = 2$, we obtain
$$\begin{array}{rl} \| \mathrm y + \mathrm c \|_2^2 &= \| \mathrm y \|_2^2 + 2 \, \mathrm c^\top \mathrm y + \| \mathrm c \|_2^2\\ &\leq 4 + 4 \| \mathrm c \|_2 + \| \mathrm c \|_2^2\\ &= \left( 2 + \| \mathrm c \|_2 \right)^2\end{array}$$
If $\rm c = (1,-1)$, then the maximum of the original problem is $\left( 2 + \sqrt 2 \right)^2$.
