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Chapter 1: Q 28. (page 50)

In Problem, (a) find the center h,kand radius rof each circle; (b) graph each circle; (c) find the intercepts, if any.

x2+y2-6x+2y+9=0

Short Answer

Expert verified

(a) Center is 3,-1and radius is 1unit.

(b) Graph is as follows;

(c) x-intercept is 3,0and no y-intercept.

Step by step solution

01

Step 1. Given information

An equation of a circle isx2+y2-6x+2y+9=0.

02

Step 2. Center and radius of a circle.

Consider the equation of a circle: x2+y2-6x+2y+9=0

x2-2路3路x+32-32+y2+2路1路y+12-12+9=0(x-3)2-9+(y+1)2-1+9=0(x-3)2+(y+1)2=1

The above equation is standard form of the circle with radius 1 and center(3,-1).

03

Step 3. Graph of the circle.

Graph of a circle is as follows:

04

Step 4. Intercepts of a circle.

To find the x-intercepts, substitute y=0and solve for x.

(x-3)2+(0+1)2=12(x-3)2+1=1x-3=0x=3

Therefore, the x-intercept is 3,0.

To find the y-intercepts, substitute x=0and solve for y.

(0-3)2+(y+1)2=129+(y+1)2=1(y+1)2=-8

Note that square of a number is never negative. Therefore, this equation has no solution and there are no yintercepts.

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