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 m
ACB. 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. All rights reserved. 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 Copyright © by Holt, Rinehart and Winston. 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 Copyright © by Holt, Rinehart and Winston. All rights reserved.    !  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 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° 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)  4
2 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 Copyright © by Holt, Rinehart and Winston. All rights reserved. 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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