 # Find the overlapping area of two equations also give its Carol Gates 2021-09-25 Answered
Find the overlapping area of two equations also give its geometrical representation: $$\displaystyle{u}^{{{2}}}+{v}^{{{2}}}={n}{\quad\text{and}\quad}{u}^{{{2}}}+{\left({v}-{n}\right)}^{{{2}}}={1}$$ put $$\displaystyle{n}={516}$$

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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.