chapter 10 answers · chapter 10 answers (continued) 34 answers algebra 2chapter 10 18. hyperbola;...

Algebra 2 Chapter 10 Answers 33

Chapter 10 Answers

Practice 10-11. (0, 0); (43, 0), (0, 43); {x∆-3 # x # 3}, {y∆-3 # y # 3} 2. (0, 0); (43, 0); {x∆x # -3 or x $ 3}, all real numbers 3. (0, 0); (41, 0), (0, 43); {x∆-1 # x # 1}, {y∆-3 # y # 3} 4. (0, 0); (43, 0), (0, 41); {x∆-3 # x # 3}, {y∆-1 # y # 1} 5. (0, 0); (43, 0), (0, 42); {x∆-3 # x # 3}, {y∆-2 # y # 2} 6. (0, 0); (45, 0), (0, 45); {x∆-5 # x # 5}, {y∆-5 # y # 5}7. ellipse;

x-axis, y-axis;{x∆-2 # x # 2},{y∆-1 # y # 1}

8. ellipse;x-axis, y-axis;{x∆-1 # x # 1},{y∆-2 # y # 2}


10. hyperbola;x-axis, y-axis;{x∆x # -2 or x $ 2},all real numbers



13. circle;all lines through center;{x∆-3 # x # 3},{y∆-3 # y # 3}

14. circle;all lines through center;{x∆ # x # },{y∆ # y # }


16. ellipse;x-axis, y-axis;{x∆ # x # },{y∆-1 # y # 1}

17. hyperbola;x-axis, y-axis;{x∆x # or x $ },all real numbers

"22"2

y

�3 3

�3

O x

3

�1

1

1�1 2

2

�2

�2

"22"2

y

�3 3

�3

O x

3

2

2

�2

�2

"52"5"52"5

y

�3 3

�3

O x

3

�1

1

1�1

"22"2"22"2

y

�3 3

�3

O x

3

1

2

2

�2

�2

y

O x

�1

1

1�1 2

2

�2

�2

y

�6 6

�6�4

O�2 2

x2

64

�2

y

�3

O x

3

�1

1

1�1 2

2

�2

�2

y

�3 3

�3

O x

3

�1

1

1�1

2

�2

y

�3 3O x

�1

1

1�1

2

�2

y

�3 3

�3

O x

3

1

1 2�2 �1

y

�3 3

�3

O x

3

2

2

�2

�2

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Chapter 10 Answers (continued)

Answers Algebra 2 Chapter 1034

18.hyperbola;x-axis, y-axis;all real numbers,{y∆y # -1 or y $ 1}

19. hyperbola;x-axis, y-axis;{x∆x # or x $ },all real numbers



22. hyperbola;x-axis, y-axis;all real numbers,{y∆y # -3 or y $ 3}


24. circle;

all lines through center;

{x∆ # x # },

{y∆ # y # }






y

�3 3

�3

O x

3

�1

1

1�1 2

2

�2

�2

y

�6 6

�6�4

x2

64

�4 4�2

y

�6 6

�6

O x

6

4

4

�4

�4

y

�6 6

�6

O x

6

�2

2

2�2

y

�9 9

�9�6

�3 3x3

96

�6 6�3

1321

3

1321

3

y

O x

32

3�2

3�2

32

y

�6 6

�6�4

�2 2x2

64

�4 4�2

O

y

�6 6

�6�4

O�2 2

x2

64

�4 4�2

y

�6 6

�6

O x

6

�2

2

2�2

4

�4

y

�6 6

�6

O x

6

�2

2

2�2 4

4

�4

�4

"52"5

y

�3 3

�3

O x

3

�1

1

1�1 2

2

�2

�2

y

�3 3

�3

O x

3

�1

1

1�1 2

2

�2

�2

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41. ellipse;x-axis, y-axis;{x∆ # x # },{y∆ # y # }22"322"3

"22"2

y

�3 3O x

�1

1

1�1 2

2

�2

�2

y

�3

O x

3

�1

1

1�1 2�2

"32"3"32"3

y

�3 3

�3

O x

3

�1

1

1�1 2�2

�2

y

�4O x

�2

2

2�2 4

4

�4

y

�3 3

�3

O x

3

�1

1

1�1

y

�6 6

�6�4

O�2 2

x2

64

�4 4�2

y

�6 6

�6�4

O�2 2

x2

64

�4 4�2

y

�6 6

�6�4

O�2 2

x2

64

�4 4

y

�3 3

�3

O x

3

�1

1

1�1 2

2

�2

�2

y

�6 6

�6

O x

6

2�2 4�4

y

�6 6

�6�4

�2 2x2

64

�4 4�2

y

�6 6O x

6

�2

2

2�2 4

4

�4

�4

�8 8

8

�8

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Practice 10-2

1. left 2. downward 3. left 4. upward 5. upward

6. left 7. right 8. downward 9. (0,-8); y = 8

10. ; y =

11. 12.

13. 14.

15. 16.

17. (2,-3); x = -2 18.

19. (0, 2); y = -2 20.

21. x = 22. y = x2 23.

24. 25. 26.

27. 28. 29.

30. 31. 32.

33. 34. 35.

36. 37. 38.

39. 40. 41.

42. 43. 44.

45a. 45b. 12.5 in. 46. 47. y = x2

48. (3,-1); (3,-2); y = 0

49. (0, 0); ; x = -

50. (-1, 1); (0, 1); x = -2

Practice 10-3

1. (x + 5)2 + (y + 2)2 = 16 2. (x - 1)2 + (y - 4)2 = 4

3. (x + 2)2 + (y - 5)2 = 1 4. (x + 4)2 + (y + 1)2 = 4

5. (x + 3)2 + (y + 4)2 = 9 6. (x - 4)2 + (y - 6)2 = 1

7. x2 + y2 = 9 8. x2 + (y - 1)2 = 4 9. (x + 1)2 + y2 = 36

10. (x - 2)2 + y2 = 1 11. x2 + (y + 3)2 = 25

12. (x - 4)2 + (y + 4)2 = 2.25 13. (x + 2)2 + (y - 6)2 = 16

14. (x - 5)2 + (y + 1)2 = 1.21 15. (x - 1)2 + (y + 5)2 = 6.25

16. (x - 2)2 + (y - 3)2 = 17. (x - 4)2 + (y + 2)2 = 9

18. (x + 2)2 + (y - 5)2 = 12 19. (x - 1)2 + (y - 7)2 = 49

20. (x - 5)2 + (y - 5)2 = 1 21. x2 + (y - 10)2 = 25

22. (x + 8)2 + (y + 6)2 = 36 23. (-1, 8); 1 24. (0,-3); 3

25. (-3,-1); 26. (6, 0); 27. (6, 9); 2 28. (0, 0); 12

29. 30.

x�8�4 4 8 12�12

O

y

�8�12�16

48

x�12 �4 4�20

O

y

�8�12

84

12

"5"2

14

O

2

�2 2

�2

x

y4

O

2

�2

�2

2x

y

18a1

8, 0b

O

�2

�4

�6

2 4xy

y 5 18x2y 5 1

40x2

x 5 112y2y 5 1

20x2x 5 120y2

y 5 2 112x2x 5 2 1

40y2x 5 214y2

x 5 2 112y2y 5 1

4x2y 5 2 116x2

x 5 124y2x 5 1

4y2y 5 132x2

y 5 128x2y 5 1

20x2x 5 2 120y2

x 5 2 124y2x 5 1

12y2y 5 112x2

x 5 18y2y 5 2 1

12x2y 5 2 116x2

x 5 2 112y21

16218y2

a0, 132b ; y 5 2 1

32

a 132, 0b ; x 5 2 1

32

a2 112, 0b ; x 5 1

12a0, 2234b; y 5 231

4

a 120, 0b ; x 5 2 1

20a0, 2 112b ; y 5 1

12

a 148, 0b ; x 5 2 1

48a34, 0b ; x 5 23

4

132a0, 2 1

32b

y

�3 3

�3

O x

�1

1

1 2

2

�2

�2

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31. 32.

33. 34.

35. 36.

Practice 10-41. ; 2. ;

3. ; 4. (46, 0);

5. ; 6. ;

7. (44, 0); 8. ;

9. ; 10. ;

11. ; 12. ;

13. ; 14. ;

x

y

O1 2�1�2

1

3

�3

�1

x

y

O1 3�1�3

12

�2�1

Q4"5, 0RQ0, 4"5R

x�2�1 21 3�3

O

y

�3�2

21

3

x�4�2 42 6�6

O

y

�6�4

42

6

Q4"5, 0RQ0, 44"3R

x�8�4 84 12�12

O

y

�12�8

84

12

x�6�3 63 9�9

O

y

�9�6

63

9

Q43"13, 0RQ46"2, 0R

x�4�2 42 6�6

O

y

�6�4

42

6

x�4�2 42 6�6

O

y

�6�4

42

6

Q0, 4"21R

x�8�4 84 12�12

O

y

�12�8

84

12

x�4�2 42 6�6

O

y

�6�4

42

6

Q0, 44"5RQ0, 472"3R

x�6�3 63 9�9

O

y

�9�6

63

9

x�6�3 63 9�9

O

y

�9�6

63

9

Q0, 4"91R

x�4�2 42 6�6

O

y

�6�4

42

6

x�6�3 63 9�9

O

y

�9�6

63

9

Q0, 4"35RQ0, 43"5R

x�4 161284�8

O

y

�12�8

�16

48

x�8 84�16

O

y

�8�12

84

12

x�8 84�16

O

y

�12�8

�16

48

x161284�8�4

O

y

�8

1284

16

x�12 �4 4�20

O

y

�8�12

84

12

x�4 84 12 16�8

O

y

�8�12�16

48

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15. ; 16. ;

17. ; 18. ;

19. ; 20. ;

21. ;

22. 23.

24. 25. 26.

27. 28.

29. 30. 31.

32. 33.

34. 35.

36. 37.

38. 39. 40.

41. 42. 43.

44. 45. 46.

47. 48. 49.

50. or

Practice 10-5

1. ; 2. ;

3. ; 4. ;

5. ; 6. ;

2

�6

46

�4�2�4 2 4 6�6

x

y

O2

�6

46

�4�2�4 2 4 6�6

x

y

O

Q42"17, 0RQ4"10, 0R

O

8

�8

�8

8x

y

O

8

�8

�8

8x

y

Q0, 42"10RQ4"85, 0R

2

�6

46

�4�2�4 2 4 6�6

x

y

O2

�6

46

�4�2�4 2 4 6�6

x

y

O

Q0, 4"34RQ42"2, 0R

x2

2500 1y2

10,000 5 1x2

10,000 1y2

2500 5 1

x2

4 1 y2 5 1x2

49 1y2

25 5 1x2 1y2

5 5 1

x2

18 1y2

9 5 1x2

26 1y2

25 5 1x2

20 1y2

16 5 1

x2

121 1y2

100 5 1x2

81 1y2

36 5 1x2

20 1y2

4 5 1

x2

16 1y2

32 5 1x2

16 1y2

4 5 1x2 1y2

4 5 1

x2

36 1y2

20.25 5 1x2

400 1y2

625 5 1

x2

196 1y2

100 5 1x2

100 1y2

196 5 1

x2

49 1y2

100 5 1x2

36 1y2

25 5 1

x2

9 1y2

18 5 1x2

5 1y2

4 5 1x2

4 1 y2 5 1

x2

0.25 1y2

2.25 5 1x2

16 1y2

25 5 1

x2

10 1 y2 5 1x2 1y2

5 5 1x2

29 1y2

4 5 1

x2

16 1y2

4 5 1x2

81 1y2

16 5 1

xO1 3�1�3

12

�1�2

Q0, 42"2R

x

y

O1 3�1�3

32

�3�2

x

y

O2 3�2�3

32

�3�2

Q4"2, 0RQ4"2, 0R

x

y

2 4 6�2�4�6

6

�6

x

y

O3 6�3�6

69

�9�6

Q0, 42"6RQ4"65, 0R

x

y

O2 4 6�2�4�6

42

�2�4

y

O1 2�1�2

23

�3�2

Q0, 4"11RQ4"15, 0R

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7. (0, 45); 8. ;

9. ; 10. (0, 45);

11. ; 12. ;

13. ; 14. ;

15. ; 16. ;

17. ; 18. ;

19. ; 20. ;

21. ; 22. ;

23. ; 24. ;

25. ; 26. ;

x

y

O4 62�4�6 �2

642

�6

�2�4

x

y

O4 62�4�6 �2

6

2

�6

�2

Q45"2, 0RQ0, 42"5R

x

y

O4 62�4�6 �2

6

2

�6

�2

x

y

O63�6�3

963

�9�6�3

Q0, 44"2RQ44"5, 0R

O

6

�6

�6

6

x

y

x

y

O64�6�4

642

�6�4�2

Q4"37, 0RQ42"5, 0R

x

y

642�6�4�2

64

�6�4

x

y

O642�6�4�2

64

�6�4

Q4"17, 0RQ0, 4"13R

x

y

O642�6�4�2

6

24

�6�4�2

x

y

64�6�4

6

24

�6�4�2

Q0, 4"41RQ0, 4"10R

x

y

O2 4�2�4

6

24

�6�4�2

O

8

�8

�8

8x

y

Q4"29, 0RQ4"26, 0R

2

�6

46

�4

�2�4 2 4x

y

O

4

�4

�4 2�2 4 6�6x

y

O

6

�6

Q0, 45"2RQ0, 4"29R

O

10

�10

�10

10x

y

4

�4

�12

812

�8

�8 4�4 8 12�12x

y

O

Q0, 42"26RQ4"73, 0R

2

�6

46

�4�2�4 2 4 6�6

x

y

O2

�6

46

�4�2�4 2 4 6�6

x

y

O

a0, 45"52 b

2

�6

46

�4�2�4 2 4 6�6

x

y

O2

�6

46

�4�2�4 2 4 6�6

x

y

O

Q4"13, 0R

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27. ; 28. (0, 45);

29. ; 30. ;

31. ; 32. ;

33. ; 34. ;

35. ; 36. ;

37. ; 38. (45, 0);

39. ; 40. ;

41. ; 42. ;

43. ; 44. ;

45. ;

46. x2

1.869 3 1011 2y2

3.752 3 1012 5 1

x

y

O64�6�4

6

24

�6�4�2

Q42"17, 0R

x

y

O642�6�4�2

6

2

�6

�2

x

y

O642�6�4�2

42

�4�2

Q0, 42"5RQ0, 4"29R

x

y

O642�6�4�2

642

�6�4�2

x

y

6�6

642

�6�4�2

Q43"5, 0RQ0, 4"17R

x

y

O42 6�6�4�2

642

�6�4�2

x

y

O42 6�6�4�2

64

�6�4

Q4"41, 0RQ0, 42"5R

x

y

O42 6�6�4�2

6

24

�6�4�2

x

y

O42 6�6�4�2

6

2

�6

�2

Q0, 4"10R

x

y

O4 6�6�4

6

24

�6�4�2

x

y

O2 6�6 �2

6

24

�6�4�2

Q4"13, 0RQ4"13, 0R

x

y

O42 6�6�4�2

6

2

�6

�2

x

y

O42 6�6�4�2

642

�6�4�2

a0, 4254 ba0, 425

4 b

x

y

O4 6�6�4

642

�6�4�2

O

8

�8

�8

8x

y

Q42"5, 0RQ4"26, 0R

x

y

O2�2

642

�6

�2�4

x

y

O4 62�4�6 �2

64

�6�4

Q4"10, 0RQ0, 4"13R

x

y

O4 62�4�6 �2

64

�6�4

x

y

O4 6�4�6

642

�6

�2�4

Q4"29, 0R

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47.

48. 49.

50. 51.

52. 53.

54. 55. 56.

57. 58. 59.

60. 61.

Practice 10-6

1. ellipse; (-1, 2); 2. hyperbola; (0, 2);

; ;

3. ellipse; (-4, 0); 4. circle; (4, 2); 1;

;

5. circle; (0,-3); 6; 6. hyperbola; (5,3); ;

7. hyperbola; (3, 2); 8. circle; (0, 0); ;(8, 2), (-2, 2);

9. circle; (-1,-7); 9; 10. hyperbola; (-1,-1);

;

11. circle; (2, 2); 3; 12. ellipse; (2,-1);

;

13. circle; (5,-2); 6; 14. circle; (-1, 5); 8;

15. parabola; (1, 2); 16. parabola; (-3,-2);

�6 2 4�8x

6

y

O

8

�4

8

42

�4 2�2 4 6�6

y

xO

963

�3 6 9�9x

y

O

152

4

�6

62 8 10

y

xO

4

�8

1

�3

1 32 4 5�1

y

xO

2

�4

1

32

2

5�1

x

4

y

O

5

Q2 4 "6, 21R

2

�6

�6 �2

�4

4�8

y

xO

4

�8�12

y

�9�6

�6 3�3 9xO

3

�15

Q21 4 "34, 21R

2

�2

1

1

�1 2 3�3x

y

O

3

�3

6

y

6

2

2 8

4

4 10�2xO

8

�4

"7

4

4

2

62 8 10�2

x

y

O

8

�4

2

�6

�4

�4

2�2 4 6x

y

O

4

�8

Q5 4 "5, 3R

2

�2

31 2

1

4 5�1x

y

O

3

�3

6

�6

�6 6�12x

y

O

9

�9

Q24 4 4"3, 0R

4

�4

�4 2

2

�2 4 6�6x

y

O

6

�6

4

�4

�4 2

2

4 6�6x

y

O

6

�6

Q4"10, 2Ra21 42"30

5 , 2b

x2

81 2y2

63 5 1x2

64 2y2

36 5 1

x2

9 2y2

40 5 1x2 2y2

80 5 1x2

36 2y2

28 5 1

x2

36 2y2

64 5 1x2

36 2y2

45 5 1x2

64 2y2

336 5 1

x2

5625 2y2

26,775 5 1x2

4489 2y2

3975 5 1

x2

5.858 3 107 2y2

1.667 3 107 5 1x2

25 2y2

200 5 1

x2

8.582 3 1010 2y2

4.812 3 1010 5 1x2

49 2y2

32 5 1

x2

3.112 3 1010 2y2

3.907 3 1012 5 1

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17. circle; (-4,-1); 4; 18. hyperbola; (0, 0);

;

19. parabola; (2,-1); 20. parabola; (2,-1);

21. (x + 4)2 + (y - 5)2 = 36

22.

23. 24. x = (y + 2)2 + 1

25. 26.

27. (x + 1)2 + (y - 2)2 = 36 28. y = -(x + 1)2 + 5

29.

30.

31.

32.

Reteaching 10-11. ; ellipse;

x-axis, y-axis;{x∆-2 # x # 2},{y∆-5 # y # 5}

2. ; circle;all lines through center;{x∆-6 # x # 6},{y∆-6 # y # 6}

3. ; hyperbola;x-axis, y-axis;{x∆x # -2 or x $ 2},all real numbers

4. ; circle;all lines through center,{x∆-3 # x # 3};{y∆-3 # y # 3}

5. ; ellipse;x-axis, y-axis;{x∆-2 # x # 2},{y∆-3 # y # 3}

6. ; hyperbola;x-axis, y-axis;{x∆x # -4 or x $ 4},all real numbers

Reteaching 10-21. 2.

x

y

O1 3�1�3

21

3

�2�3

(0, � )32

y � 32

x

y

O1 2 3�1�3�2

21

3

�2�3

(0, 1)

y ��1

x

y

O2 6�2�6

42

6

�4�2

�6

(�4, 0)(4, 0)

x

y

O4 6�4�6

46

�4�6

(�2, 0)

(0, 3)

(2, 0)

(0, �3)

x

y

O4 6�4�6

46

2

�4�6

(0, 3)(3, 0)

(0, �3)

(�3, 0)

x

y

O4 6�4�6

46

2

�2�4�6

(�2, 0) (2, 0)

x

y

O42�4�2

4

�2�4

(0, 6)

(�6, 0)

(0, �6)

(6, 0)

x

y

O4 6�4�6

2

6

�2

�6

(0, 5)

(2, 0)

(0, �5)

(�2, 0)

x2

2.25 1(y 1 2)2

6.25 5 1

(x 2 125)2

36 2y2

15,589 5 1

(x 2 2)2

25 1(y 1 5)2

16 5 1

(x 2 2)2

4 2(y 2 2)2

5 5 1

(x 1 4)2

9 1(y 1 5)2

4 5 1x2

9 1(y 2 2)2

4 5 1

12

(x 2 50)2

2304 2y2

196 5 1

(y 2 5)2

4 2(x 1 4)2

5 5 1

�2

2

4

4

6 8�4x

y

O64 8 10

xO2

�6

46

�4�2

y

4

�4

�4

2

�2 4 6�6x

y

O

6

�6

4

�4�2�6 2�10x

y

O

6

�6

Q42"2, 0R

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3. 4.

5. 6.

Reteaching 10-31. 3; (5, 2) 2. 2 ; (-8, 4) 3. 2 ; (4,-3) 4. ; (3, 0) 5. 5; (0, 5) 6. 1; (-6,-7) 7. 6; (-1,-2) 8. 2; (2, 5) 9. 2; (0, 0) 10. 3; (1,-3) 11. 2 ; (2, 3) 12. 5; (-1, 3)

13. ; (0,-3) 14. ; (-4, 0) 15. ; (-2, 6)

16. ; (7,-3) 17. ; (4,-1) 18. 9; (-9, 9)

Reteaching 10-4

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11.

12. 13.

14. 15.

16.

Reteaching 10-51. ; 2. ;

3. ; 4. ;

5. ; 6. ;

Reteaching 10-61. parabola; 2. ellipse;

y = - (x - 1)2 + 1

3. hyperbola; 4. circle;

(x + 5)2 + (y - 3)2 = 16

O

4

�4�8x

y

8

O

2

�2 2�4

�2

x

y4

(x 1 1)2

4 2(y 2 2)2

9 5 1

O

2

�2�4

�2

x

y4

O

2

�2

�2

2x

y

(x 1 3)2

4 1(y 2 1)2

1 5 114

x

y

O2 64�2�4�6

246

�6�4�2

x

y

O1 3�1�3

123

�3�2�1

Q0, 4"34RQ4"6, 0R

x

y

O1 32

1

�3

�1

3

�1�2�3x

y

O2 3�2�3

123

�3�2�1

Q0, 4"5RQ4"5, 0R

x

y

O42 6�4�6 �2

2

6

�6

�2

x

y

O4�4 6�2 2�6

42

6

�4�2

�6

Q0, 42"5RQ4"10, 0R

x2

7569 1y2

5476 5 1

x2

20.25 1y2

64 5 1x2

25 1 y2 5 1

x2

16 1y2

12.25 5 1x2

4 1y2

36 5 1

x2

20.25 1y2

36 5 1x2

225 1y2

49 5 1

x2

9 1y2

2.25 5 1x2

2.25 1y2

100 5 1x2

81 1y2

64 5 1

x2

121 1y2

25 5 1x2

625 1y2

100 5 1x2

81 1y2

9 5 1

x2

9 1y2

25 5 1x2

4 1y2

36 5 1x2

144 1y2

169 5 1

2"63"2

5"33"73"5

Á3

Á6Á5Á2

x

y

O1�1

1

�1

( , 0)12

x ��12

x

y

1

�1

(0, )14

y ��14

O

1

�1

�1

1

0 x

y

x � �13

13

,( )x

y

O1�1

1

�1

(� , 0)34

x � 34

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5. parabola; 6. ellipse;

x = (y - 3)2

7. parabola; 8. hyperbola;

x = (y - 2)2 + 3

Enrichment 10-11. 2 2. 4 3. 1 4. 4 5. 2 6. 2 7. 2 8. 1 9. 4 10. 3 11. 2 12. 4 13. July 20, 1969; first lunar landing

Enrichment 10-21. A = /w 2. P = 2� + 2w = 100 3. A = (50 - w)w = 50w - w2 4. A = -(w - 25)2 + 6255. w = 25 yd 6. � = 25 yd 7. 625 yd2 8. square 9. 50 yd by 50 yd 10. The largest rectangle with a fixedperimeter is a square.

Enrichment 10-3CONCENTRIC; 2, 6, 5, 10, 7, 9, 3, 4, 1, 8

Enrichment 10-4

1. circle 2. on the negative x-axis, beyond the negative focus

3. midway between aphelion and perihelion 4.

5. 1 6. 7.

8. No point on the ellipse may be closer than the perihelion orfarther than the aphelion.

Enrichment 10-51. 2.

3. They are the same shape. 4. One is rotated 45° from the

other one. 5. y = x; y = -x 6. x-axis; y-axis 7. There are no x- or y-intercepts; x- and y-axes are asymptotes; It is a hyperbola rotated 45°.8. There are no x- or y-intercepts; x- and y-axes are asymptotes; It is a hyperbola rotated 45° in the opposite direction from Exercise 7.9.

10. It is the same shape but rotated 45° clockwise.

Enrichment 10-6LYNX; TIGER; LION; cat; (2, 2); (1, 1); (0, 0); (3,-2); (2,-2);

(-4,-1); (-2,-3); (5,-2); (4,-2); (3, 3); (-1,-1);

(-1,-4); (-3,-2)

Chapter ProjectActivity 1: GraphingCheck students’ work.

Activity 2: CreatingCheck students’ work.

Activity 3: AnalyzingCheck students’ work.

✔ Checkpoint Quiz 11. (0, 0); (0, 3); y = -3; 2. (0, 0); (-1, 0); x = 1;

�8�6�4�2 2�10x

y

O

642

�4�6

y

�4�2 42 6�6xO

108642

O

2

�2

�2

2x

y

O

2

�2

�2

2 x

y

O

2

�1�3

�2

1 3x

y

Åd2 1 aA 2 P2 b24x2

(A 1 P)2 1y2

d2 5 1

A 2 P2

O

2

�2

�2

2 4 x

y

O

4

8

�4 4 8 x

y

(x 2 1)2

4 2(y 1 1)2

1 5 114

O

4

�4�8x

y

8

O

2

4

�2 2 4 x

y

(x 1 8)2

1 1(y 2 6)2

4 5 118

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3. (1, 0); ; y = - ; 4. (2,-1); (1,-1); x = 3;

5. x2 + y2 = 9 6. x2 + (y - 2)2 = 64 7. (x - 5)2 + (y + 1)2 = 36 8. Shift upward five units.9. Check students’ work. 10. Answers may vary. Sampleanswer: (5,-1.5)

✔ Checkpoint Quiz 2

1. 2. 3.

4. (413, 0); 5. ;

6. (0, 45); 7. ;

8. 9. 10.

Chapter Test, Form A1. (0, 0); (45, 0), (0, 45); {x∆-5 # x # 5}, {y∆-5 # y # 5}2. (0, 0); (45, 0), (0, 43); {x∆-5 # x # 5}, {y∆-3 # y # 3}3. (0, 0); (41, 0); {x∆x # -1 or x $ 1}, all real numbers4. (0, 0); (0, 43); all real numbers, {y∆y # -3 or y $ 3}

5. ; y = -

6. ; x =

7. ; x =

8. y = x2 9. x = y2

10. y = x2 11. Answers may vary. Sample: For y = ax2,

if a . 0, then parabola opens upward; if a , 0, then parabola opens downward. For x = ay2, if a . 0, then parabola opensright; if a , 0, then parabola opens left. 12. 4; (2, 3) 13. 2 ; (0,-4) 14. 2 ; (-1, 2) 15. 5; (6, 0) 16. (x - 2)2 + (y - 4)2 = 9 17. (x - 1)2 + (y + 2)2 = 4

18. (x - 5)2 + (y + 1)2 = 19. x2 + y2 = 4

20. Answers may vary. Sample: (x - 2)2 + (y + 3)2 = 16

21. 22.

23. 24.

25. 26.

27. (45, 0) 28.

29. 30.

31. 32.

33. 34. E

35. hyperbola; center (-2, 1); 36. ellipse; center (1, 3);

foci ; foci ;

37. circle; center (2,-1); 38. parabola; vertex (2, 3);radius 2;

y8

�2

O�4�6 4 6�2 2

x2

64

y

�6 6

�6�4

O�2

x2

64

�4�2

O

4

�4 �8x

y

8

O

4

�4 4�8

�4

x

y8

Q1, 3 4 "21RQ22 4 "20, 1R

x2

11,236 2y2

13,100 5 1

x2

144 2y2

1152 5 1y2

16 2(x 2 3)2

9 5 1

x2

4 2y2

5 5 1(x 1 1)2

16 1(y 2 5)2

4 5 1

x2

4 1y2

36 5 1

Q0, 4"55RQ4"13, 0R

x2

121 1y2

1214

5 1x2

814

1y2

64 5 1

x2

9 1y2

4 5 1x2

16 1y2

25 5 1

254

Á3Á2

132

116

18

2 112a 1

12, 0b

124a2 1

24, 0b116a0, 1

16b

x2

4 2y2

16 5 1y2

9 2 x2

36 5 1y2

25 2 x2

9 5 1

O

4

�4

�4

4x

y

2

�6

46

�4�2�4 2 4 6�6

x

y

O

Q4"13, 0R

4

�12

812

�8�4�8 4 8 12�12

x

y

O4

�12

812

�8

�8�4 4 8 12�12x

y

O

Q0, 4"106Rx2

25 1y2

34 5 1x2

45 1y2

36 5 1x2

20 1y2

16 5 1

O�2�4

2

2

�2

�4

x

y

O

2

4

6

�2 2 4 x

y

12a1, 12b

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39. parabola; vertex (4,-1); 40. ellipse; center (-4, 3);

foci ;

Chapter Test, Form B1. (0, 0); (44, 0), (0, 44); {x∆-4 # x # 4}, {y∆-4 # y # 4}2. (0, 0); (44, 0), (0, 42); {x∆-4 # x # 4}, {y∆-2 # y # 2}3. (0, 0); (43, 0); {x∆x # -3 or x $ 3}, all real numbers

4. , y =

5. , x = 6. y = x2

7. y = x2 8. 2; (3, 4) 9. 7; (0, -8)

10. (x - 1)2 + (y - 3)2 = 16

11. (x + 1)2 + (y - 5)2 = 9

12. 13.

14. 15. 16.

17. 18.

19. 20.

21. 22. C

23. circle; center (3, 4); 24.parabola; vertex (-3,-1);radius 3;

25. ellipse; center (3, 2); 26. hyperbola; center (-3,-3);

foci: ; foci: ;

Alternative Assessment, Form CTASK 1 Scoring Guide:

a. I, hyperbola, (0, 43); II, parabola, (0, 0);III, circle, (43, 0) and (0, 43); IV, ellipse, (45, 0) and (0, 44)

b. ;

c. Check students’ work.

3 Student identifies each conic section correctly and givesthe correct intercepts.The equations are written in standardform with no errors. Explanation is sufficiently detailedto indicate a clear understanding of the relationshipbetween conic sections and their equations.

2 Student identifies each conic section correctly and givesthe correct intercepts. The equations are written in stan-dard form with minor errors. Explanation could includemore details to indicate a clear understanding of therelationship between conic sections and their equations.

1 Student identifies at least two of the conic sections correctly.Equations of the conic sections contain major errors.Explanation does not include enough detail to indicatean understanding of the relationship between the conicsection and its equation.

0 Student makes no attempt, or no response is given.

x2

25 1y2

16 5 1

y2

9 2 x2

4 5 1; x 5 13y2; x2 1 y2 5 9

O

�2

�2�4

�4

�6

xy

�6

O

2

�2 �4x

y4

�2

�6

Q23 4 "5, 23RQ3 4 "5, 2R

y8

�2

O�4�6 4 6�2 2

x2

y

8

�2

O�4�6 4 6�2 2

x2

64

10

x2

64 2y2

36 5 1

x2

9 2y2

16 5 1x2 2(y 2 3)2

8 5 1

y2

36 2 x2

28 5 1(x 1 2)2

4 1(y 1 3)2

16 5 1

x2

49 1y2

25 5 1Q42"29, 0RQ46"2, 0R

x2

25 1 y2 5 1x2

4 1y2

16 5 1

116

14

120a2 1

20, 0b21

8a0, 18b

O

4

8

�4�8x

y

O

4

�4

�4

4x

y

Q24 4 2"2, 3R

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TASK 2 Scoring Guide:

3 Student writes the equations in standard form with noerrors. Graphs are neatly drawn and accurate, and all arecentered on the y-axis. Student identifies all parts ofeach conic section correctly.

2 Student writes the equations in standard form with minorerrors. Graphs could be more accurate. Not all the conicsections are centered on the y-axis. Student identifies allparts of each conic section with minor errors.

1 Student writes the equations in standard form, but theycontain major errors. Graphs contain major errors. Studentdoes not identify all parts of the conic sections correctly.



y = - x2 + 16; vertex (0, 16); focus ;

directrix at y = 16

3 Student writes equation correctly. The vertex, focus, anddirectrix are identified correctly.

2 Student writes the equation of the parabola with minorerrors.The vertex, focus, or directrix are identified incorrectly.

1 Student does not write the equation of the parabola correctly. At least two of the three aspects of the parabolaare identified incorrectly.



3 Student writes the equation for a conic section correctly.Graph is neatly drawn and accurate. The translation isdone correctly. New equation is written with no errors.

2 Student writes the equation for a conic section withminor errors. Graph could be more accurate. The trans-lation is performed with minor errors. New equation iswritten with minor errors.

1 Student writes the equation for a conic section, but itcontains major errors. Graph lacks accuracy. Translationand its equation contain major errors.


Cumulative Review1. C 2. J 3. C 4. F 5. C 6. G 7. A 8. J 9. A 10. H11. D 12. H 13a. 13b. 14. Answers may vary.

Sample:

15. Check students’ work. 16. 17. 18. -4c2122

dc 1 110 2

d

(x 2 5)2

4 1(y 2 2)2

6 5 1

14

13

34

a0, 1514b1

3

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chapter 10 answers · chapter 10 answers (continued) 34 answers algebra 2chapter 10 18. hyperbola;...

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