Name
LESSON
Date
Class
Practice B
11-7 Circles in the Coordinate Plane
Write the equation of each circle.
x 2 y 2 100
(x 1)2 (y 8)2 25
(x 5)2 (y 5)2 20
1. X centered at the origin with radius 10
2. R with center R(1, 8) and radius 5
3. P with center P(5, 5) and radius 2 5
4. O centered at the origin that passes
through (9, 2)
x 2 y 2 85
5. B with center B(0, 2) that passes
through (6, 0)
x 2 (y 2)2 40
6. F with center F(11, 4) that passes
through (2, 5).
(x 11)2 (y 4)2 170
Graph each equation.
2
2
7. x y 25
8. (x 2)2 (y 1)2 4
Y
Y
X
X
9. x 2 (y 3)2 1
10. (x 1)2 (y 1)2 16
Y
Y
X
X
Crater Lake in Oregon is a roughly circular lake. The lake basin
formed about 7000 years ago when the top of a volcano exploded
in an immense explosion. Hillman Peak, Garfield Peak, and Cloudcap
are three mountain peaks on the rim of the lake. The peaks are
located in a coordinate plane at H(4, 1), G (2, 3), and C (5, 2).
Y
X
11. Find the coordinates of the center of the lake.
(1, 1)
3 mile.
12. Each unit of the coordinate plane represents __
5
Find the diameter of the lake.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
52
6 miles
Holt Geometry
Name
Date
Class
Name
Practice A
LESSON
11-7 Circles in the Coordinate Plane
1. Write the equation of a circle with center (h, k )
and radius r.
2
Write the equation of each circle.
2
Write the equation of each circle.
2
3. �D with center D(3, 3) and radius 2
4. �L with center L (�3, �3) and radius 1
5. �M with center M(0, �2) and radius 9
6. �Q with center Q (7, 0) and radius 3
2. �R with center R(�1, 8) and radius 5
�
3. �P with center P (�5, �5) and radius 2 � 5
Complete Exercises 7 and 8 to write the equation of �F with center
F (2, �1) that passes through (10, 5).
4. �O centered at the origin that passes
through (9, �2)
x 2 � y 2 � 85
5. �B with center B (0, �2) that passes
through (�6, 0)
x 2 � (y � 2)2 � 40
6. �F with center F (11, 4) that passes
through (�2, 5).
(x � 11)2 � (y � 4)2 � 170
Graph each equation.
10
(x � 2)2 � (y � 1)2 � 100
7. Use the distance formula with the two given points to find the radius of �F.
2
2
�
�
�
�
�
������
�
��
�
�
�
�
���������
��
2
2
2
9. x � (y � 3) � 1
�
��
�
��
�
������
�
�
2
8. (x � 2) � (y � 1) � 4
�
�
�
��
2
7. x � y � 25
Graph each equation. First locate the center point, and use the radius
to plot four points around the center that lie on the circle. Then draw
a circle through the four points.
2
2
2
2
10. x � y � 4
9. x � y � 16
�
x 2 � y 2 � 100
2
2
(x � 1) � (y � 8) � 25
2
(x � 5) � (y � 5)2 � 20
1. �X centered at the origin with radius 10
x 2 � y 2 � 36
(x � 3)2 � (y � 3)2 � 4
(x � 3)2 � (y � 3)2 � 1
x 2 � (y � 2)2 � 81
2
2
(x � 7) � y � 9
2. �A centered at the origin with radius 6
������
Class
Practice B
LESSON
11-7 Circles in the Coordinate Plane
(x � h) � (y � k) � r
8. Write the equation of �F.
Date
�
2
10. (x � 1) � (y � 1) � 16
�
�
��
��
�
�
������
�
�
�
�
��
11. Plot A, B, and C. Draw �ABC.
_
_
�
51
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Crater Lake in Oregon is a roughly circular lake. The lake basin
formed about 7000 years ago when the top of a volcano exploded
in an immense explosion. Hillman Peak, Garfield Peak, and Cloudcap
are three mountain peaks on the rim of the lake. The peaks are
located in a coordinate plane at H (�4, 1), G(�2, �3), and C (5, �2).
�
��
�
�
�
�
13. The intersection point of the perpendicular bisectors is the same
distance from the three points. So it is the center of a circle that
intersects A, B, and C. Find the coordinates where the fire station
should be built.
Name
Date
��
��������
�
��
12. Draw the perpendicular bisectors of AB and BC.
�������
��
�
A county planning department is meeting to choose the location of a
rural fire station. The fire station needs to be the same distance from
each of the three towns it will serve. The towns are located at A(�3, 2),
B(�3, �4), and C(1, �4). Complete Exercises 11–13 in order to find the
best location for the fire station.
�
��
�
�
�
�
��
Class
12. Each unit of the coordinate plane represents _3_ mile.
5
Find the diameter of the lake.
Practice C
LESSON
11-7 Circles in the Coordinate Plane
�
�
(1, 1)
Holt Geometry
52
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Name
6 miles
Date
Holt Geometry
Class
Reteach
LESSON
11-7 Circles in the Coordinate Plane
1. Points A, B, and C lie on the circumference of a circle. AB is
twice the radius of the circle. Find m�ACB.
Equation of a Circle
The equation of a circle with center (h, k ) and
radius r is (x � h)2 � (y � k)2 � r 2.
90°
�
�
2. Points A, B, and C lie on the circumference of a circle. The center of
the circle lies in the exterior of �ABC. Classify �ABC by its angles.
(�, � )
�
0
obtuse
Write the equation of �C with center C (2, �1) and radius 6.
(x � h)2 � (y � k)2 � r 2
Give answers in simplest radical form if necessary.
�
2
(3.4, �2.7); (8.6, 7.8)
�
r�
�
r�
�
2
2
(x2 � x1) � (y2 � y1)
��
�(1 � 3)
2
� (7 � 7)2
�
r � �4 � 2
1.
Step 2 Use the equation of a circle.
Distance Formula (x � h)2 � (y � k)2 � r 2 Equation of a circle
Substitution
(x � 3)2 � (y � 7)2 � 22 (h, k) � (3, 7)
Simplify.
(x � 3)2 � (y � 7)2 � 4 Simplify.
2.
�
7. Describe the relationship between the circle and the line in Exercise 6.
3
�
3
The line is tangent to the circle at the point (2, �3).
�
0
�
�3
�
0
3
2
3. �T with center T(4, 5) and radius 8
9. Describe the relationship between the two circles in Exercise 8.
The circles are internally tangent at the point (3, 0).
4. �B that passes through (3, 6) and has
center B (�2, 6)
(x � 2)2 � (y � 6)2 � 25
(x � 4)2 � (y � 5)2 � 64
Holt Geometry
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
71
4
(x � 3)2 � (y � 1)2 � 16
2
(x � 1) � (y � 1) � 9
(3, 0)
�
�4
�3
8. Find the intersection point(s) of the circle (x � 2)2 � y 2 � 25
2
2
and the circle x � y � 9.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
4
Write the equation of each circle.
(2, �3)
53
Simplify.
�
Write the equation of �L that has center L (3, 7) and passes through (1, 7).
6. Find the intersection point(s) of the circle (x � 2)2 � y 2 � 25
17 .
and the line y � _4_ x � ___
3
3
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
�4
Step 1 Find the radius.
� 2�19 , 7_________
� 4� 19 , 4_________
� 4�19
� 4_________
� � � 25�19 , 7_________
�
5
5
5
�
�
0
�6
You can also write the equation of a circle if you know the center
and one point on the circle.
4. Find the coordinates of all possible centers of the circle in Exercise 3.
5. Find the intersection point(s) of the circle (x � 2)2 � y 2 � 25
and the line 2x � y � 3.
6
Substitute 2 for h, �1 for k, and
6 for r.
2
(x � 2) � (y � 1) � 36
3� 5
�
Equation of a circle
(x � 2)2 � (y � (�1))2 � 6 2
3. The points X (3, 4) and Y(9, 1) lie on the circumference of a circle. There
is exactly 60° of arc between X and Y. Find the radius of the circle.
�
�
��
11. Find the coordinates of the center of the lake.
(�1, �1)
������
�
�
54
Holt Geometry
Holt Geometry