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Chapter 1: Q 9. (page 50)

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

Short Answer

Expert verified

Center is 52,2.

Radius is 32units.

Standard form of the equation isx-522+(y-2)2=94.

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.

Diameter is the distance between the points 1,2and 4,2

Diameter=(4-1)2+(2-2)2

=9+0=3

Radius=Diameter2=32

Center is the midpoint of the points 1,2and 4,2

Center=1+42,2+22=52,2

03

Step 3. Find the standard form of the equation of a circle.

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

Therefore, equation of the circle with center 52,2and radius 32is

role="math" localid="1646125761348" x-522+(y-2)2=322x-522+(y-2)2=94

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