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Chapter 1: Q 8. (page 50)

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

Short Answer

Expert verified

Center is 1,2.

Radius is equal to 2units.

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

Step by step solution

01

Step 1. Given information

Figure of a circle is 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 (1,2)and 1,0.

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

=0+4=4=2

From the given graph, we can see that the center is1,2.

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 1,2and radius 2is

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

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