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Chapter 11: Q 11.20 (page 1080)

(a) Find the center and radius, then (b) graph the circle:x2+y2+6x-2y+1=0

Short Answer

Expert verified

The center and the radius of the circle are (-3,1) and r=3respectively. The graph of this circle is:

Step by step solution

01

Part (a) Step 1. Given information.

The equation of the circle isx2+y2+6x-2y+1=0

We have to find radius and center.

Also, we have to graph this circle.

02

Part (a) Step 2. Complete the squares

Collect the x- and y- terms,

x2+y2+6x-2y+1=0x2+6x+y2-2y=-1x2+6x+9+y2-2y+1=-1+9+1(x+3)2+(y-1)2=32

03

Part (a) Step 3. Compare with the standard form of a circle to find radius and center 

Compare (x+3)2+(y-1)2=32with the standard form (x-h)2+(y-k)2=r2

We have, role="math" localid="1645269841711" (h,k)=(-3,1)(centre)

r=3(radius)

04

Part (b) Step 1. Graph the circle

The graph is:

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