No, it doesn't have anything to do with a circle, it has to do with the area of a rectangle. Could please give us the entire problem. There are an infinite number of rectangles that could be positioned as you show it.
Not a lot. First you ask for the "equasion of the shaded box". A box does not have "an equation". You might want the four inequalities that are satisfied by points in the box or you might want the area of the box. I don't know what you original problem asked for- "the equation of the shaded box" just doesn't mean anything! One problem I think you could answer is "what is the area of the largest box of this form".