Writing the Equation of a Circle

We will be using the completing the square method for this, so lets

remember…

Completing the SquarePerfect Square Trinomials:Factor:

962 xx 33 xx This is called a perfect square trinomial because

the factors are the same.

So we can rewrite these factors as: 23x

This fact is going to help us during the process of completing the square!

Completing the square method:Steps:

1. Get all variables grouped together on one side of the equation, and all the constants on the other side of the equation (if coefficient of the squared term is not one, you must divide everything by it)

2. Take half of the coefficient of the non-squared variable term, square it, and add it to both sides

3. Factor the perfect square trinomial and write it as a binomial squared

4. Square root both sides to get rid of square from the binomial (don’t forget, when introducing a square root into the problem, your constant will have a +/- in front of it

5. Solve the two equations for the variable to get your roots

#8: 0542 xx

5 5

542 xx

___5___42 xx

22

9442 xx

4 4

92 2 x

92 2 x

32 x

32x

32 x

5x

1x

Roots: 5,1

Page 3

018222 yxyx

0182 22 yyxx

182 22 yyxx

______1___8___2 22 yyxx

21 24

1 16 1 16

1641 22 yx

Group by variable

Get Constant on other side

𝐶=(1,4 )𝑟=√16=4

Page 3

0712822 yxyx

07128 22 yyxx

7128 22 yyxx

______7___12___8 22 yyxx

24 26

16 36 16 36

4564 22 yx

Group by variable

Get Constant on other side

𝐶=(4 ,−6 )𝑟=√45

Page 3

0481022 yxyx

04810 22 yyxx

4810 22 yyxx

______4___8___10 22 yyxx

25 24

25 16 25 16

4545 22 yx

Group by variable

Get Constant on other side

𝐶=(5 ,−4 )𝑟=√45

Page 3

091022 xyx

0910 22 yxx

910 22 yxx

___9___10 22 yxx

25

25 25

165 22 yx

Group by variable

Get Constant on other side

𝐶=(−5,0 )𝑟=√16=4

Writing the equation of a circle given the center and a point on the

circle:

Page 4

Steps:

1. Graph the points

2. Draw a triangle

3. Find length of radius using Pythagorean

4. Write equation of circle using center and radius.

222 cba

222 33 c

3

3299 c

218 c218 c

c18

18

222 rkyhx

222 18 yx

1822 yx 0,0:Center

18Radius

Page 4

5

222 rkyhx 222 55 yx

255 22 yx

0,5:Center

5Radius

Page 4

222 cba

222 15 c

1

5

2125 c226 c

226 c

c26

26

222 rkyhx

222 261 yx

261 22 yx

1,0:Center

26Radius

Homework

•Page 3

#2,6,8,10•Page 4

#3,5,6