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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Use the Distance Formula to show that the circle with center ( 0, 0 ) and radius length r has the equation x 2 + y 2 = r 2 .

To determine

To prove:

The circle with centre (0, 0) and radius r has the equation x2+y2=r2 using distance formula.

Explanation

The circle with the centre (0, 0) and radius r.

The above figure is circle and is drawn with centre (0, 0) and the radius r.

Let (x,y) be the points on the circle.

Hence the distance between the point (0, 0) and (x, y) points is the radius of the circle.

Using distance formula for finding the length of the radius r as below,

r=(x-0)2+(y-0)2

Simplifying the above expression as below,

r=(x)2+(y)2

Take square root on both sides of the above expression,

(r)2=

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