   Chapter 10.4, Problem 26E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

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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