Lesson 18
M5
GEOMETRY
Lesson 18: Recognizing Equations of Circles
Classwork
Opening Exercise
a.
Express this as a trinomial: (
5) .
3
3
3
b.
3
Express this as a trinomial: ( + 4) .
?
=
40
3
3
3
3
9
=
49
+ 12 + 36.
c.
Factor the trinomial:
d.
Complete the square to solve the following equation:
Lesson 18:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Recognizing Equations of Circles
+ 6 = 40.
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Lesson 18
M5
GEOMETRY
Example 1
The following is the equation of a circle with radius 5 and center (1, 2). Do you see why?
2 +1+
4 + 4 = 25
Exercise 1
1.
Rewrite the following equations in the form (
a.
b.
+4 +4+
) +(
) =
.
6 + 9 = 36
10 + 25 +
+ 14 + 49 = 4
Lesson 18:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Recognizing Equations of Circles
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Lesson 18
M5
GEOMETRY
Example 2
What is the center and radius of the following circle?
+4 +
12 = 41
Exercises 2–4
2.
Identify the center and radius for each of the following circles.
a.
20 +
b.
3 +
+ 6 = 35
5 =
19
2
Lesson 18:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Recognizing Equations of Circles
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Lesson 18
M5
GEOMETRY
3.
Could the circle with equation
4.
Stella says the equation
why not?
6 +
8 +
7 = 0 have a radius of 4? Why or why not?
+ 2y = 5 has a center of (4, 1) and a radius of 5. Is she correct? Why or
Example 3
Could
+
+
+
+
= 0 represent a circle?
Lesson 18:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Recognizing Equations of Circles
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Lesson 18
M5
GEOMETRY
Exercise 5
5.
Identify the graphs of the following equations as a circle, a point, or an empty set.
a.
+
+4 = 0
b.
+
+6
c.
2
+2
4 + 15 = 0
5 +
+
13
=0
4
Lesson 18:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
Recognizing Equations of Circles
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Lesson 18
M5
GEOMETRY
Problem Set
1.
Identify the centers and radii of the following circles.
a.
b.
( + 25) +
8 =8
20 +
c.
2.
=1
+2 +
d.
+
e.
+ +
10 + 25 = 0
= 19
+
=
1
4
Sketch graphs of the following equations.
a.
+
+ 10
4 + 33 = 0
b.
+
+ 14
16 + 104 = 0
c.
+
+4
10 + 29 = 0
3.
Chante claims that two circles given by ( + 2) + (
tangent. She is right. Show that she is.
4.
Draw a circle. Randomly select a point in the interior of the circle; label the point . Construct the greatest radius
circle with center that lies within the circular region defined by the original circle. Hint: Draw a line through the
center, the circle, and point .
Lesson 18:
© 2014 Common Core, Inc. All rights reserved. commoncore.org
4) = 49 and
Recognizing Equations of Circles
+
6 + 16 + 37 = 0 are externally
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