# The blank in the statement “The graph of the equation ( x − 1 ) 2 + ( y − 2 ) 2 = 9 is a circle with center ( , ) and radius .” ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.8, Problem 6E
To determine

## To fill: The blank in the statement “The graph of the equation (x−1)2+(y−2)2=9 is a circle with center (   ,   ) and radius         .”

Expert Solution

The complete statement is “The graph of the equation (x1)2+(y2)2=9 is a circle with center (1,2) and radius 3units.”

### Explanation of Solution

Given information:

The statement “The graph of the equation (x1)2+(y2)2=9 is a circle with center (   ,   ) and radius         .”

Consider the provided statement “The graph of the equation (x1)2+(y2)2=9 is a circle with center (   ,   ) and radius         .”

Rewrite the equation as (x1)2+(y2)2=32

The standard form of the equation of the circle is (xh)2+(yk)2=r2 , where (h,k) denote the center of the circle and r denote the radius.

Compare, (xh)2+(yk)2=r2 and (x1)2+(y2)2=32 .

Here, h=1,k=2 and r=3 .

Therefore, center of circle is (1,2) and radius is 3 .

Thus, the complete statement is “The graph of the equation (x1)2+(y2)2=9 is a circle with center (1,2) and radius 3units.”

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