Theequation of a circle whose center is at ( 2 , − 1 ) and radius is 3 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 93E
To determine

To calculate: Theequation of a circle whose center is at (2,−1) and radius is 3 units.

Expert Solution

Theequation ofthe circle is (x2)2+(y+1)2=9 .

Explanation of Solution

Given information:

The center of a circle is at (2,1) and radius is 3 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 (2,1) and radius is 3 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 (2,1) also radius r is 3.

Here, h=2,k=1 and r=3 .

Substitute the values in standard equation of circle,

(x2)2+(y(1))2=32(x2)2+(y+1)2=9

Thus, the equation of circle is (x2)2+(y+1)2=9 .

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