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## Homework Statement

I would like to know how the boundary of the inequality change when the origin of the coordinate system changes.

## Homework Equations

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

I write

$$(2x-1)^2+(2y-1)^2+z^2=4[ (x-0.5)^2+(y-0.5)^2+z^2/4] $$[/B]

but I do not know how to proceed with the problem