Name
LESSON
Date
Class
Practice C
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 mACB.
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.
Give answers in simplest radical form if necessary.
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.
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. Find the intersection point(s) of the circle (x 2)2 y 2 25
4 x ___
17 .
and the line y __
3
3
7. Describe the relationship between the circle and the line in Exercise 6.
8. Find the intersection point(s) of the circle (x 2)2 y 2 25
2
2
and the circle x y 9.
9. Describe the relationship between the two circles in Exercise 8.
Copyright © by Holt, Rinehart and Winston.
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53
Holt Geometry
Practice A
LESSON
11-7 Circles in the Coordinate Plane
1. Write the equation of a circle with center (h, k )
and radius r.
Practice B
LESSON
11-7 Circles in the Coordinate Plane
2
2
(x h) (y k) r
Write the equation of each circle.
2
Write the equation of each circle.
2
2. R with center R (1, 8) and radius 5
2
x y 36
(x 3)2 (y 3)2 4
(x 3)2 (y 3)2 1
2
2
x (y 2) 81
2
2
(x 7) y 9
2. A centered at the origin with radius 6
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
3. P with center P(5, 5) and radius 2
Complete Exercises 7 and 8 to write the equation of F with center
F (2, 1) that passes through (10, 5).
x 2 y 2 85
x (y 2) 40
6. F with center F(11, 4) that passes
through (2, 5).
(x 11) (y 4) 170
2
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
X
2
X
2
2
Y
5
5. B with center B(0, 2) that passes
through (6, 0)
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
10. x 2 y 2 4
9. x y 16
Y
4. O centered at the origin that passes
through (9, 2)
Graph each equation.
10
2
2
(x 2) (y 1) 100
7. Use the distance formula with the two given points to find the radius of F.
8. Write the equation of F.
x 2 y 2 100
2
2
(x 1) (y 8) 25
2
2
(x 5) (y 5) 20
1. X centered at the origin with radius 10
10. (x 1)2 (y 1)2 16
Y
Y
X
11. Plot A, B, and C. Draw ABC.
_
_
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).
#
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.
Y
X
6 miles
52
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All rights reserved.
Practice C
LESSON
11-7 Circles in the Coordinate Plane
#
'
12. Each unit of the coordinate plane represents _3_ mile.
5
Find the diameter of the lake.
Holt Geometry
(1, 1)
(1, 1)
(
11. Find the coordinates of the center of the lake.
51
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!
12. Draw the perpendicular bisectors of AB and BC.
Y
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.
X
Holt Geometry
Review for Mastery
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 mACB.
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°
y
r
(h, k)
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.
x
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.
(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.
2
(x 2) (y 1) 36
3 5
(3.4, 2.7); (8.6, 7.8)
5. Find the intersection point(s) of the circle (x 2)2 y 2 25
and the line 2x y 3.
Substitute 2 for h, 1 for k, and
6 for r.
Simplify.
Step 1 Find the radius.
r
r
r
6. Find the intersection point(s) of the circle (x 2)2 y 2 25
17 .
and the line y _4_ x ___
3
3
4
Step 2 Use the equation of a circle.
2
2
( x2 x1) ( y2 y1) Distance Formula (x h)2 (y k)2 r 2 Equation of a circle
2
2
(1 3) (7 7)
42
1.
Substitution
(x 3)2 (y 7)2 22 (h, k) (3, 7)
Simplify.
(x 3)2 (y 7)2 4 Simplify.
2.
y
7. Describe the relationship between the circle and the line in Exercise 6.
y
3
3
The line is tangent to the circle at the point (2, 3).
x
0
x
3
K
0
3
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
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71
001-072_Go08an_CRF_c11.indd 54
4
(x 3)2 (y 1)2 16
(x 1)2 (y 1)2 9
(3, 0)
E
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.
C
Write the equation of each circle.
(2, 3)
53
0
4
Write the equation of L that has center L (3, 7) and passes through (1, 7).
4 19 , 4_________
4 19
2 19 , 7_________
4_________
25 19 , 7_________
5
5
5
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
x
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.
2
y
6
Equation of a circle
54
Holt Geometry
Holt Geometry
4/13/07 1:40:35 PM
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