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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Geometry

Reading Strategies Use a Concept Map

Use the concept map below to help you understand circles in the coordinate plane.

Equation The equation of a circle with center (h, k) and radius r is

(x − h)2 + (y − k)2 = r 2.

Example The equation of a circle with center (2, −3) and radius 4:

(x − 2)2 + (y − (−3))2 = 42

or (x − 2)2 + (y + 3)2 = 16

Graph

Write the equation of each circle.

1. a circle with center (−2, 10) and radius 6

2. a circle with center (0, 0) and radius 3

3. a circle with center (8, 2) and radius 7

Graph each circle. 4. (x + 1)2 + (y − 5)2 = 25 5. (x − 4)2 + (y − 2)2 = 9

Circles in the Coordinate Plane

LESSON

x-x

12-5812-58

LESSON

12-7

CS10_G_MECR710624_C12L07g.indd 58 4/8/11 12:27:38 PM

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Geometry

5.

6.

7.

8.

Challenge 1, 2, 4, 6, 12.

3. AB ≈ 7.28 ≈ 7

5. a. y = 3 ± 16 − (x − 2)2; y = 5 ± 36 − (x + 5)2

b. (0.73, 6.79) c. (−1.08, 0.45) 7. AC = 4, BC = 6 8. 33° 9. 66° 10. 55° 11. 110° 13. 20.73 square units 14. 16.44 square units 15. 4.29 square units 16. 15.36 square units 17. 7.52 square units 18. 7.84 square units 19. 12.13 square units

Problem Solving 1. (x + 1)2 + (y − 4)2 = 16 2. A = 74π 3. B 4. J 5. A 6. G 7. C

Reading Strategies 1. (x + 2)2 + (y − 10)2 = 36 2. x2 + y2 = 9 3. (x − 8)2 + (y − 2)2 = 7 4.

5.

A56A56

CS10_G_MECR710624_C12_AK.indd 56 4/14/11 7:32:58 PM