# Theequation of a circle whose center is at ( − 1 , − 4 ) and radius is 8 units. ### 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 94E
To determine

## To calculate: Theequation of a circle whose center is at (−1,−4) and radius is 8 units.

Expert Solution

Theequation of the circle is (x+1)2+(y+4)2=64 .

### Explanation of Solution

Given information:

The center of a circle is at (1,4) and radius is 8 units.

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 provided conditions that center of a circle is at (1,4) and radius is 8 units.

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, (h,k) and (1,4) also radius r is 8.

Here, h=1,k=4 and r=8 .

Substitute the values in standard equation of circle,

(x(1))2+(y(4))2=82(x+1)2+(y+4)2=64

Thus, the equation of circle is (x+1)2+(y+4)2=64 .

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