Lesson 1 Contents

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Transparency 10-8
5-Minute Check on Lesson 10-7

• Find x.
• 
  2.
• 3.
  4.
• 5. Find
  x in the figure

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3
6
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Standardized Test Practice
A
C
B
D
6
8
12
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B
Click the mouse button or press the Space Bar to
display the answers.
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Lesson 10-8

• Equations of Circles

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Objectives

• Write the equation of a circle
• Graph a circle on the coordinate plane

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Vocabulary

• Circle Equation an algebraic equation that
  describes a circle

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Equations of Circles
Center at (-6,7)
Center at (6,6)
r4
r3
(x-6)2 (y-6)2 16
(x6)2 (y-7)2 9
Center at (0,0)
r2
x2 y2 4
Center at (8,-6)
Center at (-7,-7)
r2
r1
(x-8)2 (y6)2 1
(x7)2 (y7)2 4
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Example 8-1a
Equation of a circle
Simplify.
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Example 8-1b
Equation of a circle
Simplify.
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Example 8-1c
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Example 8-2a
Sketch a drawing of the two tangent lines.
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Example 8-2b
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Example 8-2b
The center is at (4, 2), and the radius is 5.
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Example 8-2c
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Example 8-3a
Compare each expression in the equation to the
standard form.
The center is at (2, 3), and the radius is 2.
Graph the center. Use a compass set at a width
of 2 grid squares to draw the circle.
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Example 8-3b
Answer
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Example 8-3c
Write the expression in standard form.
The center is at (3, 0), and the radius is 4.
Draw a circle with radius 4, centered at (3, 0).
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Example 8-3d
Answer
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Example 8-3e
Answer
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Example 8-3f
Answer
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Example 8-4a
ELECTRICITY Strategically located substations
are extremely important in the transmission and
distribution of a power companys electric
supply. Suppose three substations are modeled by
the points D(3, 6), E(1, 0), and F(3, 4).
Determine the location of a town equidistant from
all three substations, and write an equation for
the circle.
Explore You are given three points that lie on a
circle.
Plan Graph ?DEF. 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.
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Example 8-4b
Solve Graph ?DEF and construct the
perpendicular bisectors of two sides. The center
appears to be at (4, 1). This is the location of
the tower. Find r by using the Distance Formula
with the center and any of the three points.
Write an equation.
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Example 8-4e
AMUSEMENT PARKS The designer of an amusement
park wants to place a food court equidistant from
the roller coaster located at (4, 1), the Ferris
wheel located at (0, 1), and the boat ride
located at (4, 3). Determine the location for
the food court and write an equation for the
circle.
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Summary Homework

• Summary
• The coordinates of the center of a circle (h, k)
  and its radius r can be used to write an equation
  for the circle in the form (x h)2 (y k)2
  r2
• A circle can be graphed on a coordinate plane by
  using the equation written in standard form
• A circle can be graphed through any three
  noncollinear points on the coordinate plane
• Homework
• pg 578 10-17, 25-27