Alg2 Ch10 HW - StartLogicwellsmat.startlogic.com/.../alg2_ch10_hw.pdf · 2 Lesson 10-1 pages...

1

Chapter 10

Homework

2

Lesson 10-1

pages 538–541 Exercises

1.

Hyperbola: center (0, 0),

y-intercepts at ± , no

x-intercepts, the lines of

symmetry are the x- and

y-axes; domain: all real

numbers, range: y

or y .

10-1

2.

Ellipse: center (0, 0), x-intercepts at ±3 2,

y-intercepts at ±6, the lines of symmetry

are the x- and y-axes; domain:

– 3 2 x 3 2, range –6 y 6.

5 3

3

5 3

35 3

3

<– <– <– <–

>–

<–

3

3.

Circle: center (0, 0), radius 4,

x-intercepts at ±4, y-intercepts

at ±4, there are infinitely many

lines of symmetry; domain:

–4 x 4, range: –4 y 4.

4.

Hyperbola: center (0, 0), y-intercepts

at ± 3, no x-intercepts, the lines of

symmetry are the x- and y-axes; domain:

all real numbers, range: y 3 or y 3.

5.

Ellipse: center (0, 0), y-intercepts

at ±2, x-intercepts at ±5, the lines

of symmetry are the x- and y-axes;

domain: –5 x 5, range: –2 y 2.

6.

Circle: center (0, 0), radius 7, x- and

y-intercepts at ±7, there are infinitely

many lines of symmetry; domain:

–7 x 7, range: –7 y 7.

<– <–<– <–

<– <– <– <–

<– <– <– <–>–<–

Lesson 10-1

410-1

7.

Hyperbola: center (0, 0), y-intercepts

at ±1, the lines of symmetry are the

x- and y-axes; domain: all real numbers,

range: y –1 or y 1.

8.

Hyperbola: center (0, 0), x-intercepts

at ±2, the lines of symmetry are the

x- and y-axes; domain: x –2 or x 2,

range: all real numbers.

9.

Circle: center (0, 0), radius 10, x- and

y-intercepts at ±10, there are infinitely

many lines of symmetry; domain:

–10 x 10, range: –10 y 10.

10.

Circle: center (0, 0), radius 2, x- and

y-intercepts at ±2, there are infinitely

many lines of symmetry; domain:

–2 x 2, range: –2 y 2.

>–<–

>–<– <– <–<– <–

<– <– <– <–

Lesson 10-1

5

Lesson 10-1

10-1

11.

Ellipse: center (0, 0), x-intercepts

at ±4, y-intercepts at ±2, the lines

of symmetry are the x- and y-axes;

domain: –4 x 4, range: –2 y 2.

12.

Circle: center (0, 0), radius 5, x-

and y-intercepts at ± 5, there are

infinitely many lines of symmetry;

domain: – 5 x 5,

range: – 5 y 5.

13.

Ellipse: center (0, 0), x-intercepts at ±1,

y-intercepts at ± , the lines of symmetry

are the x- and y-axes; domain:

–1 x 1, range: y .

1

3

1

3

1

3

<– <– <– <–

<– <–<– <–

<– <– <– <–

6

Lesson 10-1

14.

Hyperbola: center (0, 0), x-intercepts

at ±6, the lines of symmetry are the

x- and y-axes; domain: x –6 or x 6,

range: all real numbers.

15.

Hyperbola: center (0, 0), y-intercepts at ± ,

the lines of symmetry are the x- and y-axes;

domain: all real numbers, range: y – or y .

16.

Ellipse: center (0, 0), x-intercepts

at ±2, y-intercepts at ±6, the lines of

symmetry are the x- and y-axes;

domain: –2 x 2, range: –6 y 6.

17. center (0, 0), x-intercepts at ±3,

y-intercepts at ±2; domain: –3 x 3,

range: –2 y 2

10-1

1

2

1

2

1

2

<– <–

<– <–

<– <– <– <–

>–<–

>–<–

7

Lesson 10-1

10-1

18. center (0, 0), no x-intercepts,

y-intercepts at 42; domain:

all real numbers, range: y –2 or y 2

19. center (0, 0), x-intercepts at 43,

no y-intercepts; domain: x –3 or x 3,

range: all real numbers

20. center (0, 0), x-intercepts at 48,

y-intercepts at 44; domain: –8 x 8,

range: –4 y 4

21. center (0, 0), x-intercepts at 43,

y-intercepts at 45; domain: –3 x 3,

range: –5 y 5

22. center (0, 0), no x-intercepts,

y-intercepts at 43; domain:

all real numbers; range: y –3 or y 3

23. 19

24. 17

25. 18

26. 20

27. 21

28. 22

29.

Hyperbola: center (0, 0), x-intercepts

±4, the lines of symmetry are the x-

and y-axes; domain: x –4 or x 4,

range: all real numbers.

>–<–

>–<–

>–<–

<– <–<– <–

<– <–<– <–

>–<–

8

Lesson 10-2

25

4

25

4

24. (0, 0), (6, 0), x = –6

25. (0, 0), (0, –1), y = 1

26. (0, 0), (3, 0), x = –3

27. (0, 0), , 0 , x = –25

4

25

4

28. (0, 0), (0, 1), y = –1

29. (0, 0), (0, –1), y = 125

4

25

4

25

4

25

4

910-2

30. (2, 0), (2, 1), y = –1

31. (0, 0), (–2, 0), x = 2

32. (–2, 4), –2, , y =

33. (–3, 0), – , 0 , x = –

34. (4, 0), (4, –6), y = 6

35. (3, –1), (6, –1), x = 0

17

4

15

4

3

2

9

2

Lesson 10-2

10

36. x = y2

37. y = x2

38. y = – x2

39. x = – y2

40. x = – y2

41. y = – x2

42.

1

12

1

400

1

20

1

28

1

36

5

56

43. x = – y2

44. y = x2

45. x = y2

46.

47.

1

8

1

4

48.

49.

50.

Lesson 10-2

1110-3

24. (–6, 0), 11

25. (–2, –4), 16

26. (3, 7), 4 6

27.

28.

29.

30.

31.

32.

33.

34.

Lesson 10-3

12

Lesson 10-3

pages 552–554 Exercises

1. x2 + y2 = 100

2. (x + 4)2 + (y + 6)2 = 49

3. (x – 2)2 + (y – 3)2 = 20.25

4. (x + 6)2 + (y – 10)2 = 1

5. (x – 1)2 + (y + 3)2 = 100

6. (x + 5)2 + (y + 1)2 = 36

7. (x + 3)2 + y2 = 64

8. (x + 1.5)2 + (y + 3)2 = 4

9. x2 + (y + 1)2 = 9

10. (x + 1)2 + y2 = 1

11. (x – 2)2 + (y + 4)2 = 25

12. (x + 1)2 + (y – 3)2 = 81

13. x2 + (y + 5)2 = 100

14. (x – 3)2 + (y – 2)2 = 49

15. (x + 6)2 + (y – 1)2 = 20

16. (x – 5)2 + y2 = 50

17. (x + 3)2 + (y – 4)2 = 9

18. (x – 2)2 + (y + 6)2 = 16

19. (1, 1), 1

20. (–2, 10), 2

21. (3, –1), 6

22. (–3, 5), 9

23. (0, –3), 5

10-3

1310-3

66. parabola; x = (y + 2)2 + 3;

67. Let P(x, y) be any point on the circle

centered at the origin and having radius r.

If P(x, y) is one of the points (r, 0), (–r, 0),

(0, r), or (0, –r), substitution shows that

x2 + y2 = r 2. If P(x, y) is any other point on

the circle, drop a perpendicular PK from P to

the x-axis (K on the x-axis). OPK is a right

triangle with legs of lengths |x| and |y| and

with hypotenuse of length r. By the

Pythagorean Theorem, |x|2 + |y|2 = r 2.

But |x|2 = x2 and |y|2 = y2. So x2 + y2 = r 2.

58. (0, 4), 11

59. (–5, 0), 3 2

60. (–2, –4), 5 2

61. (–3, 5), 38

62. (–1, 0), 2

63. (3, 1), 6

64. (0, 2), 2 5

65. circle; (x – 4)2 + (y – 3)2 = 16;

Lesson 10-3

14

pages 559–561 Exercises

1. + = 1

2. + y2 = 1

3. + y2 = 1

4. x2 + = 1

5. + = 1

6. + = 1

7. + = 1

8. + = 1

9. + = 1

Lesson 10-4

10. + = 1

11. + = 1

12. + = 1

13. + = 1

14. x2 + = 1

15. + = 1

16. + = 1

17. x2 + = 1

x 2

16

y 2

9

x 2

4

x 2

9

y 2

36

x 2

16

y 2

49

x 2

36

y 2

25

x 2

81

y 2

4

x 2

9

y 2

25

x 2

2.25

y 2

0.25

x 2

64

y 2

256

x 2

36

y 2

100

x 2

12.25

y 2

25

x 2

196

y 2

49

y 2

16

y2

12.25x 2

256

x 2

900

y 2

400

y 2

6.25

18. (0, 5), (0, – 5)

19. (0, 4), (0, –4)

15

22. (0, 6), (0,–6)

23. (0, 6), (0, – 6)

20. (4 2, 0), (–4 2, 0)

21. (8, 0), (–8, 0)

24. (2 3, 0), (–2 3, 0)

25. (9, 0), (–9, 0)

Lesson 10-4

16

26. (3 15, 0), (–3 15, 0)

27. + = 1

28. + = 1

29. + = 1

30. + = 1

31. + = 1

32. + = 1

x 2

64

y 2

64x 2

100

y 2

128

x 2

89

y 2

64

x 2

4

y 2

20

y 2

49x 2

245y 2

225x 2

514

33. ( 5, 0), (– 5, 0)

34. (0, 2 3), (0, –2 3)

35. (0, 4 2), (0, –4 2)

36. (0, 21), (0, – 21)

37. (0, 2 7), (0, –2 7)

38. (0, 1), (0, –1)

39. (–3, 8), (–3, 2)

40. (–2, 2), (–2, – 2)

41. a. 0.9;

b. 0.1;

c. The shape is close

to a circle.

d. The shape is close

to a line segment.

10-4

Lesson 10-4

17

42. + = 1

43. a.Yes; since c2 = a2 – b2, if the

foci are close to 0, then c2 will

be close to 0 and a2 will be close

to b2. This means a will be close

to b and hence the ellipse will be

close to a circle.

b. If F1 and F2 are considered distinct

pts., then a circle is not an ellipse.

If F1 and F2 are the same pt., then

a circle is an ellipse.

44. + = 1

45. + y2 = 1

46. x2 + = 1

x 2

16

y 2

4

x 2

9

y 2

4

y 2

9

x 2

20.2547. + = 1

48. The vertices are the points farthest

from the center and the co-vertices

are the points closest to the center.

49. Check students’ work.

50. + = 1

51. + = 1

52. + = 1

53. + = 1

54. + = 1

55. + = 1

x 2

4

y 2

16

x 2

4

y 2

3

x 2

25

y 2

4

y 2

81x 2

121

x 2

702.25

y 2

210.25

y 2

144x 2

169y 2

324x 2

256

10-4

Lesson 10-4

18

3.

4.

Lesson 10-5

pages 566–568 Exercises

1.

2.

5.

6.

10-5

19

7.

8.

9.

10. (0, 97), (0, – 97)

11. (0, 113), (0, – 113)

12. ( 265, 0), (– 265, 0)

10-5

Lesson 10-5

20

19. – = 1

20. – = 1

21. – = 1

22. – = 1

23. – = 1

24. – = 1

25. y2 – = 1

26. – y2 = 1

x 2

9

y 2

16

x 2

69,169

y 2

96,480

x 2

144

x 2

192,432,384

y 2

170,203,465

x 2

240,000

y 2

10,000

x 2

1.865 × 1012

y 2

5.270 × 1011

y 2

25

x 2

3

x 2

4

27.

28.

29.

30. – = 1

31. – x2 = 1

y 2

20.25

x 2

4

y 2

9

10-5

Lesson 10-5

21

Lesson 10-6

pages 573–576 Exercises

1. + = 1

2. + = 1

3. + = 1

4. + = 1

5. – = 1

6. – = 1

7. – = 1

8. – = 1

9. – = 1

(x + 2)2

9

(y – 1)2

4

(x – 5)2

16

(y – 3)2

36

(x – 3)2

9

(y + 6)2

49

x 2

36

(y + 4)2

25

(x + 3)2

16

(y + 3)2

9

(y + 3)2

4

(x – 4)2

32

(x + 1)2

9

(y – 2)2

40

(y + 1)2

25

(x + 1)2

56

(y – 1)2

25x 2

16

10. – = 1

11. – = 1

12. y = (x – 4)2 + 3; parabola, vertex (4, 3)

13. (x + 6)2 + y2 = 81; circle, center (–6, 0), radius 9

(x – 150)2

1296

y 2

21,204

(x – 175)2

1936

y 2

28,689

10-6

22

14. + = 1; ellipse,

center (–1, 3), foci (–1, 3 ± 6 )

15. (x – 1)2 + (y + 3)2 = 13; circle,

center (1, –3), radius 13

(x + 1)2

3

(y – 3)2

9 16. (y – 2)2 – (x – 3)2 = 1; hyperbola,

center (3, 2), foci (3, 2 ± 2)

17. – (y + 1)2 = 1; hyperbola,

center (1, –1), foci (1 ± 5 , –1)

(x – 1)2

4

10-6

Lesson 10-6

2310-6

18. x2 + (y + 7)2 = 36; circle,

center (0, –7), radius 6

19. x – 3 = (y – 2)2; parabola,

vertex (3, 2)

1

2

20. + = 1; ellipse,

center (–2, 3), foci (–2 ± 5, 3)

21. (x + 3)2 – (y – 5)2 = 1; hyperbola,

center (–3, 5), foci (–3 ± 2, 5)

(x + 2)2

9

(y – 3)2

4

Lesson 10-6

24

(x – 1)2

16

y 2

4y 2

822. + = 1; ellipse,

center (1, 0), foci (1 ± 2 3, 0)

23. – = 1; hyperbola,

center (0, –3), foci (± 13, –3)

x2

4

(y + 3)2

9

24. Translate the equation – = 1,

a hyperbola centered at (0, 0), 3 units left.

25. a. hyperbola

b. line

26. a. h is added to each x-coordinate,

and k is added to each y-coordinate.

b. The lengths of the major and minor axes

are unchanged; the x-coordinates of the

vertices are increased (or decreased) by

the same amount, and the same is true

for the y-coordinates. A similar remark

holds for the co-vertices.

x2

16

10-6

Lesson 10-6