Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Write an equation of a circle with the given center and radius. Check your answers.

7. center (0, 0), radius 10
8. center ( − 4 , − 6 ) , open negative 4 comma negative 6 close comma  radius 7
9. center (2, 3), radius 4.5
10. center ( − 6 , 10 ) , open negative 6 comma 10 close comma  radius 1
11. center ( 1 , − 3 ) , open 1 comma negative 3 close comma  radius 10
12. center ( − 1.5 , − 3 ) , open negative 1.5 comma negative 3 close comma  radius 2

See Problem 2.

Write an equation for each translation.

13. x 2 + y 2 = 9 ; x squared , plus . y squared , equals 9 semicolon  down 1 unit
14. x 2 + y 2 = 1 ; x squared , plus . y squared , equals 1 semicolon  left 1 unit
15. x 2 + y 2 = 25 ; x squared , plus . y squared , equals 25 semicolon  right 2 units and down 4 units
16. x 2 + y 2 = 81 ; x squared , plus . y squared , equals 81 semicolon  left 1 unit and up 3 units
17. x 2 + y 2 = 100 ; x squared , plus . y squared , equals 100 semicolon  down 5 units
18. x 2 + y 2 = 49 ; x squared , plus . y squared , equals 49 semicolon  right 3 units and up 2 units
19. An archery target has a circular bull's-eye (diameter 24 cm) surrounded by four concentric rings, each with a width of 12 cm. Draw the target in a coordinate plane with center at the origin. Write the equations of the circles that form the boundaries of the different regions of the target.

See Problem 3.

Write an equation for each circle. Each interval represents one unit.

See Problem 4.

For each equation, find the center and radius of the circle.

22. ( x − 1 ) 2 + ( y − 1 ) 2 = 1 open x minus 1 close squared . plus . open y minus 1 close squared . equals 1
23. ( x + 2 ) 2 + ( y − 10 ) 2 = 4 open x plus 2 close squared . plus . open y minus 10 close squared . equals 4
24. ( x − 3 ) 2 + ( y + 1 ) 2 = 36 open x minus 3 close squared . plus . open y plus 1 close squared . equals 36
25. ( x + 3 ) 2 + ( y − 5 ) 2 = 81 open x plus 3 close squared . plus . open y minus 5 close squared . equals 81
26. x 2 + ( y + 3 ) 2 = 25 x squared , plus . open y plus 3 close squared . equals 25
27. ( x + 6 ) 2 + y 2 = 121 open x plus 6 close squared . plus . y squared , equals 121

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