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Chapter 1: Q 7. (page 50)

Find the center and radius of the circle. Write the standard form of the equation.

Short Answer

Expert verified

Center is 2,1.

Radius is equal to 2units.

Standard form of the equation is(x-2)2+(y-1)2=4.

Step by step solution

01

Step 1. Given information

Figure of a circle is given as follows:

02

Step 2. Find the center and radius of a circle.

Radius is the distance between the center and any point on the circle

In this case, radius is the distance between the points (0,1)and (2,1)

Radius=(0-2)2+(1-1)2

=4+0=4=2

From the given graph, we can see that the center is 2,1.

03

Step 3. Find the standard form of the equation.

Equation of a circle with center h,kand radius ris (x-h)2+(y-k)2=r2

Therefore, equation of the circle with center 2,1and radius 2is

(x-2)2+(y-1)2=22(x-2)2+(y-1)2=4

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Most popular questions from this chapter

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

x+13鈥�+x+27=5

Find the distance d(P1,P2)between the points P1andP2.

P1=(-4,-3);P2=(6,2)

Plot each pair of points and determine the slope of the line containing them. Graph the line by hand.

(-3,-1);(2,-1)

If two distinct lines have the same slope, but different x-intercepts, can they have the same y-intercept?

Find the distance d(P1,P2)between the points P1andP2.

P1=(a,a);P2=(0,0)
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