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Chapter 11: Q 11.19 (page 1080)

(a) Find the center and radius, then (b) graph the circle: x2+y2-6x-8y+9=0

Short Answer

Expert verified

The center and the radius of the circle are (3,4) and 4respectively. 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-8y+9=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-8y+9=0x2-6x+y2-8y=-9x2-6x+9+y2-8y+16=-9+9+16(x-3)2+(y-4)2=16

03

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

Compare (x-3)2+(y-4)2=16with role="math" localid="1645268784417" (x-h)2+(y-k)2=r2

We have, (h,k)=(3,4)(centre)

andr=4(radius)

04

Part (b) Step 1. Graph the circle

The graph is:

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