See Problem 5.

Use the center and the radius to graph each circle.

28. ( x + 4 ) 2 + ( y − 4 ) 2 = 4 open x plus 4 close squared . plus . open y minus 4 close squared . equals 4
29. ( x − 6 ) 2 + y 2 = 64 open x minus 6 close squared . plus , y squared , equals 64
30. x 2 + y 2 = 9 x squared , plus . y squared , equals 9
31. ( x + 3 ) 2 + ( y − 9 ) 2 = 49 open x plus 3 close squared . plus . open y minus 9 close squared . equals 49
32. ( x − 7 ) 2 + ( y − 1 ) 2 = 100 open x minus 7 close squared . plus . open y minus 1 close squared . equals 100
33. x 2 + ( y + 4 ) 2 = 144 x squared , plus . open y plus 4 close squared . equals 144

B Apply

Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.)

34. (0, 4)
35. ( 0 , − 3 ) open 0 comma negative 3 close
36. ( − 5 , 0 ) open negative 5 comma 0 close
37. ( 3 , 0 ) open square root of 3 comma 0 close
38. ( 4 , − 3 ) open 4 comma negative 3 close
39. ( 12 , − 5 ) open 12 comma negative 5 close
40. ( − 2 , 3 ) open negative 2 comma 3 close
41. ( 1 , − 5 ) open 1 comma negative 5 close
42. ( − 6 , − 4 ) open negative 6 comma negative 4 close

43. Think About a Plan Three gears of radii 6 in., 4 in., and 2 in. mesh with each other in a motor assembly as shown below. What is the equation of each circle in standard form?

    
    Image Long Description

    • How can the diagram of the gears in the coordinate plane help you solve this problem?
    • How can you write an equation for each circle?
44. Open-Ended Write two functions that together represent a circle.

Use the given information to write an equation of the circle.

45. radius 7, center ( − 6 , 13 ) open negative 6 comma 13 close
46. area 25 π , 25 pi comma  center ( 5 , − 3 ) open 5 comma negative 3 close
47. center ( − 2 , 7.5 ) , negative 2 comma 7.5 close comma  circumference 3 π 3 pi
48. center ( 1 , − 2 ) , open 1 comma negative 2 close comma  through (0, 1)
49. center (2, 1), through (6, 4)
50. center (6, 4), through (2, 1)
51. translation of ( x − 1 ) 2 + ( y + 3 ) 2 = 36 , 2 open x minus 1 close squared . plus . open y plus 3 close squared . equals 36 comma 2  units left and 4 units down
52. Machinery Three gears, A, B, and C, mesh with each other in a motor assembly. Gear A has a radius of 4 in., B has a radius of 3 in., and C has a radius of 1 in. If the largest gear is centered at ( − 7 , 0 ) , negative 7 comma 0 close comma  the smallest gear is centered at (4, 0), and Gear B is centered at the origin, what is the equation of each circle in standard form?

Find the center and the radius of each circle.

53. x 2 + y 2 = 2 x squared , plus . y squared , equals 2
54. x 2 + ( y + 1 ) 2 = 5 x squared , plus . open y plus 1 close squared . equals 5
55. x 2 + y 2 = 14 x squared , plus . y squared , equals 14
56. x 2 + ( y − 4 ) 2 = 11 x squared , plus . open y minus 4 close squared . equals 11
57. ( x + 5 ) 2 + y 2 = 18 open x plus 5 close squared . plus . y squared , equals 18
58. ( x + 2 ) 2 + ( y + 4 ) 2 = 50 open x plus 2 close squared . plus . open y plus 4 close squared . equals 50
59. ( x + 3 ) 2 + ( y − 5 ) 2 = 38 open x plus 3 close squared . plus . open y minus 5 close squared . equals 38
60. x 2 + 2 x + 1 + y 2 = 4 x squared , plus 2 x plus 1 plus . y squared , equals 4
61. x 2 + y 2 − 6 x − 2 y + 4 = 0 x squared , plus , y squared , minus 6 x minus 2 y plus 4 equals 0
62. x 2 + y 2 − 4 y − 16 = 0 x squared , plus , y squared , minus 4 y minus 16 equals 0

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