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High School
Geometry
High school geometry
Circles

Carol Gates

Answered question

2021-09-25

Find the overlapping area of two equations also give its geometrical representation:

u^{2} + v^{2} = n and u^{2} + {(v - n)}^{2} = 1

put

n = 516

Answer & Explanation

Viktor Wiley

Skilled2021-09-26Added 84 answers

Step 1 The equation of the form

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

u^{2} + v^{2} = n f or n = 516

gives a circle with center at (0,0) and radius approximately 22.7156. The equation

u^{2} + {(v - n)}^{2} = 1 f or 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.

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