I would like to know how the boundary of the inequality change when the origin of the coordinate system changes.
The original inequality is[/B]
$$ r_0 \le x^2+y^2+z^2 \le R^2$$
I would like to know the boundary of the following term, considering the previous inequality
$$ (2x-1)^2+(2y-1)^2+z^2 $$
The Attempt at a Solution
$$(2x-1)^2+(2y-1)^2+z^2=4[ (x-0.5)^2+(y-0.5)^2+z^2/4] $$[/B]
but I do not know how to proceed with the problem