Step 1
The equation of the form \(\displaystyle{x}^{{2}}+{y}^{{2}}={r}^{{2}}\) is the standard equation of a circle with radius r. To obtain the overlapping area the intersection of the circles should be obtained.
Step 2
The function \(\displaystyle{u}^{{2}}+{v}^{{2}}={n}{f}{\quad\text{or}\quad}{n}={516}\) gives a circle with center at (0,0) and radius approximately 22.7156. The equation \(\displaystyle{u}^{{2}}+{\left({v}−{n}\right)}^{{2}}={1}{f}{\quad\text{or}\quad}{n}={516}\) gives an circle with center at (0, 516) and radius 1. Therefore, these circles do not intersect and hence the overlapping area is 0.
Step 3
These equations do not intersect and hence the overlapping area is 0.