Equations Of Circles Worksheet - Chapter 10-8 Page 3
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2
3
4
5
6Study Tip
A Circle Through Three Points
Example
Example
4
4
L0cus
CELL PHONES
Cell phones work by the transfer of phone signals from one
The center of the circle is
tower to another via satellite. Cell phone companies try to locate towers so that
the locus of points
they service multiple communities. Suppose three large metropolitan areas are
equidistant from the three
modeled by the points A(4, 4), B(0,
12), and C( 4, 6), and each unit equals
given points. This is a
100 miles. Determine the location of a tower equidistant from all three cities,
compound locus because
and write an equation for the circle.
the point satisfies more
than one condition.
Explore
You are given three points that lie on a circle.
Plan
Graph
ABC. Construct the perpendicular bisectors of two sides to
locate the center, which is the location of the tower. Find the length of
a radius. Use the center and radius to write an equation.
Solve
Graph
ABC and construct the
perpendicular bisectors of two
y
C
( 4, 6 )
sides. The center appears to be at
( 2,
3). This is the location of the
( 4, 4 )
A
tower.
Find r by using the Distance
Formula with the center and any
O
x
of the three points.
2
2
r
[ 2
4]
[ 3
4]
( 2,
3 )
85
Write an equation.
2
2
2
[x
( 2)]
[y
( 3)]
85
2
2
(x
2)
(y
3)
85
B
( 0,
12 )
Examine You can verify the location of the center by finding the equations of
the two bisectors and solving a system of equations. You can verify the
radius by finding the distance between the center and another of
the three points on the circle.
Concept Check
1.
OPEN ENDED
Draw an obtuse triangle on a coordinate plane and construct the
circle that circumscribes it.
2. Explain how the definition of a circle leads to its equation.
Guided Practice
Write an equation for each circle.
3. center at ( 3, 5), r
10
4. center at origin, r
7
5. diameter with endpoints at (2, 7) and ( 6, 15)
Graph each equation.
2
2
2
2
6. (x
5)
(y
2)
9
7. (x
3)
y
16
8. Write an equation of a circle that contains M( 2,
2), N(2,
2), and Q(2, 2).
Then graph the circle.
Lesson 10-8 Equations of Circles 577
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