Graphing Circles

Viviana C. CastellónEast Los Angeles College

MEnTe

Mathematics Enrichment

through Technology

Standard form of an equation of a circle

where (h,k) is the center of the circle and r is the radius

2 2 2x h y k r

General from of the equation of a circle

2 2 0x y ax by c

where a, b, and c are variables

Graphing a circle whose equation is in general form

Since the equation given is in the general form, completing the square will be used. By completing the square, the equation can then be set-up in the standard form of an equation of a circle therefore, identifying its center and radius.

2 2 6 2 9 0x y x y

Center (3,-1)

Radius 1

2 2

2 2

2 2

2 2

22 21

6 2 9 0

6 + 2 9

6 9 1 92 9

3 1

3

1

1

1

x y x y

x x y y

x x y y

x y

x y

Since the radius = 1, use the center (3,-1) as a reference point and then move 1 point to the left, right, up and down.

Graph the following equation

2 2 6 4 9 0x y x y

Center (-3,-2)

Radius 2

2 2

2 2

2 2

2 2

2 2 23 2

6 4 9 0

6 + 4 9

6 4 9

3 2 4

9 4 9 4

2

x y x y

x x y y

x x y y

x y

x y

Since the radius = 2, use the center (-3,-2) as a reference point and then move 2 points to the left, right, up and down.

Graph the following equation

2 2 10

2x y x y

2 2

2 2

2 2

2 2

2 21 1

2 2

1 1 1

10

21

+ 21

+ 2

1 1 + 1

2 2

+

1

4

1

4 4 4

x y x y

x x y y

x x y y

x y

x y

Center

Radius 1

1 1,

2 2

Since the radius = 1, use the center

as a reference point and then move 1 point to the left, right, up and down.

1 1,

2 2

Graph the following equation

2 22 2 8 7 0x y x

2 2

2 2

2 2

2 2

2 2

2 2

2 22

2 2 8 7 0

2 4 + 2y 7

4 2y 7

2 2 2y 1

2 2 2y 1

2 4 8

21

2 y 2

2 2

10

2

x y x

x x

x x

x

x

x

x y

Recall: 8 was obtained when multiplied by 2 and 4

Center

Radius 2,0

Since the radius = ,

use the center

as a reference point and then move point to the left, right, up and down.

1

2

12

2,0

12

Congratulations!!You just completed

Graphing Circles