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Chapter 11: Q. 45 (page 1083)

In the following exercises, (a) identify the center and radius and (b) graph.

x2+y2+6y+5=0

Short Answer

Expert verified

(a) The center and radius of the graph x2+y2+6y+5=0is (0,-3)and r=2

(b) The graph of the function is:

Step by step solution

01

Part (a) Step 1. Given

The function x2+y2+6y+5=0

To find the radius and center of the circle.

02

Part (a) Step 2. Group x,y-terms

Group the x-terms and y-terms. Collect the constants on the right side.

x2+y2+6y+5=0x2+(y2+6y)=5

03

Part (a) Step 3. Complete the squares.

Complete the squares and write in binomial form.

x2+(y2+6y+9)-9=-5x2+(y+3)2=4

04

Part (a) Step 4. Identify the center and radius.

Identify the center and radius by comparing the equation with standard form of circle (x-h)2+(y-k)2=r2.

From the equation, the center is (0,-3)and the radius is 2

05

Part (b) Step 1. Given

The function x2+y2+6y+5=0

To graph the function

06

Part (b) Step 2. Graph the function

Graph the circle with center (0,-3)and radius 2

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