# Thecenter and radius of the circle x 2 + ( y − 2 ) 2 = 4 and sketch the graph of the circle.

### 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 90E
To determine

Expert Solution

## Answer to Problem 90E

The center of the circle is (0,2) and radius is 2 units. The graph of the circle is provided below,

### Explanation of Solution

Given information:

The equation x2+(y2)2=4 .

Formula used:

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.

Calculation:

Consider the equation x2+(y2)2=4 .

Rewrite the equation as,

(x0)2+(y2)2=22

Recall that 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 (x0)2+(y2)2=22 .

Here, h=0,k=2 and r=2 .

Therefore, center of circle is (0,2) and radius is 2 .

Now, on the Cartesian plane construct a circle with center at (0,2) and radius 2 units.

The graph obtained is provided below,

Thus, the center of the circle is (0,2) and radius is 2 units.

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