Chapter 10 Circles - 10.6 Equations Of Circles Worksheet Page 2
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GOAL
2
G
C
RAPHING
IRCLES
If you know the equation of a circle, you can graph the circle by identifying its
center and radius.
Graphing a Circle
E X A M P L E 3
S
H
TUDENT
ELP
Study Tip
2
2
The equation of a circle is (x + 2)
+ (y º 3)
= 9. Graph the circle.
You can sketch the graph
of the circle in Example 3
Rewrite the equation to find the center and radius:
y
without a compass by
first plotting the four
2
2
(x + 2)
+ (y º 3)
= 9
points shown in red.
2
2
2
[x º (º2)]
+ (y º 3)
=
3
Then sketch a circle
( 2, 3)
through the points.
The center is (º2, 3) and the radius is 3. To
graph the circle, place the point of a compass at
1
(º2, 3), set the radius at 3 units, and swing the
1
x
compass to draw a full circle.
Applying Graphs of Circles
E X A M P L E 4
A bank of lights is arranged over a stage. Each
T
L
HEATER
IGHTING
light illuminates a circular area on the stage. A coordinate plane is used
to arrange the lights, using the corner of the stage as the origin. The equation
2
2
(x º 13)
+ (y º 4)
= 16 represents one of the disks of light.
a.
Graph the disk of light.
Three actors are located as follows: Henry is at (11, 4), Jolene is at (8, 5), and
b.
Martin is at (15, 5). Which actors are in the disk of light?
S
OLUTION
Rewrite the equation to find the center and radius:
a.
2
2
(x º 13)
+ (y º 4)
= 16
2
2
2
(x º 13)
+ (y º 4)
=
4
The center is
(13, 4)
and the radius is 4. The circle is shown below.
y
Jolene
(8, 5)
1
1
x
The graph shows that Henry and Martin are both in the disk of light.
b.
10.6 Equations of Circles
637
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