Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write the standard equation of each circle.

8. center ( 2 , − 8 ) ; r = 9 open 2 comma negative 8 close semicolon , r equals 9
9. center ( 0 , 3 ) ; r = 7 open 0 comma 3 close semicolon , r equals 7
10. center ( 0.2 , 1.1 ) ; r = 0 . 4 open 0.2 comma 1.1 close semicolon , r equals 0 . , 4
11. center ( 5 , − 1 ) ; r = 12 open 5 comma negative 1 close semicolon , r equals 12
12. center ( − 6 , 3 ) ; r = 8 open minus , 6 comma 3 close semicolon , r equals 8
13. center ( − 9 , − 4 ) ; r = 5 open minus , 9 comma negative 4 close semicolon , r equals , square root of 5
14. center ( 0 , 0 ) ; r = 4 open 0 comma 0 close semicolon , r equals 4
15. center ( − 4 , 0 ) ; r = 3 open minus , 4 comma 0 close semicolon , r equals 3
16. center ( − 1 , − 1 ) ; r = 1 open minus , 1 comma negative 1 close semicolon , r equals 1

See Problem 2.

Write a standard equation for each circle in the diagram below.

Image Long Description

17. ⊙ P circle dot p
18. ⊙ Q circle dot q

Write the standard equation of the circle with the given center that passes through the given point.

19. center ( − 2 , 6 ) ;  point  ( − 2 , 10 ) open minus , 2 comma 6 close semicolon , point . open minus , 2 comma 10 close
20. center (1, 2); point (0, 6)
21. center ( 7 , − 2 ) ;  point  ( 1 , − 6 ) open 7 comma negative 2 close semicolon , point , open 1 comma negative 6 close
22. center ( − 10 , − 5 ) ;  point  ( − 5 , 5 ) open minus , 10 comma negative 5 close semicolon , point . open minus , 5 comma 5 close
23. center (6, 5); point (0, 0)
24. center ( − 1 , − 4 ) ;  point  ( − 4 , 0 ) open minus , 1 comma negative 4 close semicolon , point . open minus , 4 comma 0 close

See Problem 3.

Find the center and radius of each circle. Then graph the circle.

25. ( x + 7 ) 2 + ( y − 5 ) 2 = 16 open x plus . 7 , close squared , plus , open y minus . 5 , close squared . equals 16
26. ( x − 3 ) 2 + ( y + 8 ) 2 = 100 open x minus . 3 , close squared , plus , open y plus . 8 , close squared . equals 100
27. ( x + 4 ) 2 + ( y − 1 ) 2 = 25 open x plus . 4 , close squared , plus , open y minus . 1 , close squared . equals 25
28. x 2 + y 2 = 36 x squared , plus , y squared , equals 36

Public Safety Each equation models the position and range of a tornado alert siren. Describe the position and range of each.

29. ( x − 5 ) 2 + ( y − 7 ) 2 = 81 open x minus . 5 , close squared , plus , open y minus . 7 , close squared . equals 81
30. ( x + 4 ) 2 + ( y − 9 ) 2 = 144 open x plus . 4 , close squared , plus , open y minus . 9 , close squared . equals 144

B Apply

Write the standard equation of each circle.

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