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Graph the equation. Identify the radius of the circle.

1. x2 1 y2 5 9 2. x2 1 y2 5 20 3. x2 1 y2 5 64

x

y

1

1

x

y

2

2

x

y

4

4

4. x2 1 y2 5 50 5. 5x2 1 5y2 5 80 6. 3x2 1 3y2 5 120

x

y

4

4

x

y

2

2

x

y

2

2

Write the standard form of the equation of the circle with the given radius and whose center is the origin.

7. Ï}

7 8. 2 Ï}

5 9. 3 Ï}

10

Write the standard form of the equation of the circle that passes through the given point and whose center is the origin.

10. (2, 3) 11. (23, 5) 12. (4, 26)

The equations of both circles and parabolas are given. Graph the equation.

13. x2 1 3y 5 0 14. 2x2 1 2y2 5 8 15. x2 2 8y 5 0

x

y2

2

x

y

1

1

x

y

2

2

Write an equation of the line tangent to the given circle at the given point.

16. x2 1 y2 5 17; (1, 4) 17. x2 1 y2 5 52; (24, 6)

18. Capitol Dome The Capitol Dome sits atop the Capitol Building in Washington, D.C. The base of the dome is circular with a diameter of 96 feet. Suppose a coordinate plane was placed over the base of the dome with the origin at the center of the dome. Write an equation in standard form for the outside boundary of the dome.

Practice BFor use with the lesson “Graph and Write Equations of Circles”

Les

so

n 8

.3

Algebra 2Chapter Resource Book8-28

Lesson

8.3

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Lesson Graph and Write Equations of Parabolas, continued 5. y2 5 4x 6. x2 5 8y 7. y2 5 212x

8. x2 5 212y 9. x2 5 20y; 2.45 m

Interdisciplinary Application

1. right 2. (7, 0); x 5 27

3. y

x3

3

4. x2 5 30y 5. 4.8 ft

Challenge Practice

1. a. 64 Ï

}

2 }

3

b. As p approaches 0, the parabola becomes narrower and narrower. So, the area A becomes smaller and smaller.

2. {(x, y)y 5 4x 2 2}

3. a. x 5 t2, y 5 t

b. t 23 22 21 0 1 2 3

x 9 4 1 0 1 4 9

y 23 22 21 0 1 2 3

c.

x

y

x

y

4

4

t 5 22t 5 23

t 5 0

t 5 2t 5 3

t 5 1

t 5 21

d.

x

y

x

y

2

4

The graphs are the same.

4. a. x2 5 2640y b. 8 ft

Lesson Graph and Write Equations of CirclesTeaching Guide

1. a circle

2.

x

y

5

5

(10, 0), (0, 10), (210, 0), (0, 210); 10 feet

3. Sample answer: (6, 8), (8, 6)

Practice Level A

1. B 2. C 3. A

4.

x

y

2

2

5.

x

y

2

2

1 5

6.

x

y

3

3

7.

x

y

2

2

9 2 Ï}

3

8.

x

y

2

2

9.

x

y

4

4

Ï}

30 Ï}

110

10. x2 1 y2 5 9 11. x2 1 y2 5 36

12. x2 1 y2 5 10 13. x2 1 y2 5 1

14. x2 1 y2 5 8 15. x2 1 y2 5 13

16. y 5 2 2 } 3 x 1

13 }

3 17. y 5 2x 1 10 18. yes

Practice Level B

1.

x

y

1

1

2.

x

y

2

2

3 2 Ï}

5

Algebra 2Chapter Resource BookA36

8.2

8.3

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Lesson Graph and Write Equations of Circles, continued 3.

x

y

4

4

4.

x

y

4

4

8 5 Ï}

2

5.

x

y

2

2

6.

x

y

2

2

4 2 Ï}

10

7. x2 1 y2 5 7 8. x2 1 y2 5 20

9. x2 1 y2 5 90 10. x2 1 y2 5 13

11. x2 1 y2 5 34 12. x2 1 y2 5 52

13.

x

y2

4

14.

x

y

1

1

15.

x

y

2

2

16. y 5 2 1 } 4 x 1

17 }

4 17. y 5

2 }

3 x 1

26 }

3

18. x2 1 y2 5 2304

Practice Level C

1.

x

y

5

5

2.

x

y

2

2

10 6

3.

x

y

3

3

4.

x

y

2

2

7 2 Ï}

6

5.

x

y

2

2

6.

x

y

2

2

3 Ï}

2 2 Ï}

7

7. x2 1 y2 5 13 8. x2 1 y2 5 28

9. x2 1 y2 5 272 10. x2 1 y2 5 20

11. x2 1 y2 5 14 12. x2 1 y2 5 101

} 4

13. y 5 3 }

2 x 2

13 }

2 14. y 5

2 Ï}

6 }

2 x 1 10

15. 6.93 16. 20

Study Guide

1.

x

y

2

2

; 4 2.

x

y

3

3

; 9

3.

x

y

1

1

; 3

4. x2 1 y2 5 13 5. y 5 2 1 } 2 x 1 5

6. The customer does not qualify for free delivery.

Problem Solving Workshop: Worked Out Example

1. no 2. yes 3. about 63 mi 4. yes 5. yes

6. no

Algebra 2Chapter Resource Book A37

8.3