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Chapter 11: Q. 44 (page 1069)

In the following exercises, 鈸� identify the center and radius, and 鈸� graph.

x2+y2+12x-14y+21=0

Short Answer

Expert verified

(a) Center of the circlex2+y2+12x-14y+21=0islocalid="1645125277424" (-6,7)and radius is 8

(b) Graph of the circle is

Step by step solution

01

Step 1. given data 

The given equation of the circle is

x2+y2+12x-14y+21=0

02

Step 2. Part (a) 

Group the x-terms and y-terms

x2+y2+12x-14y+21=0x2+12x+y2-14y=-21

complete the squares

x2+12x+36+y2-14y+49=-21+36+49x+62+y-72=64

Compare the equation with the standard equation of the circle

x-(-6)2+y-72=82x-h2+y-k2=r2

so center(h,k)=(-6,7)

radiusr=8

03

Step 3. Part (b) 

Plot the circle of center (-6,7)and radius8

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