<s>[INST] 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?
 [/INST] Hint
You found
$$(x-1)^2+(y+1)^2=4$$
which is the equation of a circle centered in $(1,-1)$ and with radius $2$. 
The function $x^2+y^2$ is the square of the distance of $(x,y)$ to the origin. Which point $(x,y)$ on this circle is located the furthest from the origin? It helps to make a simple sketch.

Alternatively, you can handle this as a constrained optimization problem and use for example the method of Lagrange multipliers.
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