CK- 12 Algebra II with Trigonometry Concepts 1

Transcription

1 10.1 Parabolas with Verte at the Origin Answers 1. up. left 3. down 4.focus: (0, -0.5), directri: = focus: (0.065, 0), directri: = focus: (-1.5, 0), directri: = focus: (0, ), directri: = - ans CK- 1 Algebra II with Trigonometr Concepts 1

2 8.focus: (0.15, 0), directri: = ans focus: (0, -0.75), directri: = 0.75 ans = 16 = 40 = p =, p and a have an inverse relationship. 4a 14.see worked out solution ke inches above the verte CK- 1 Algebra II with Trigonometr Concepts

3 10. Parabolas with Verte at (h, k) Answers 1.verte: (-1, 6), focus: (-1, 5.5), directri: = 6.75, ais: = -1.verte: (3, 7), focus: (3, 7.5), directri: = 6.75, ais: = 3 3.verte: (-1, -), focus: (1, -), directri: = -3, ais: = - 4.verte: (3, 0), focus: (0.5, 0), directri: = 5.5, ais: = 0 5.verte: (-6, -8), focus: (-6, -7), directri: = -9, ais: = -6 6.verte: (0, 5), focus: (-0.15, 5), directri: = 0.15, ais: = 5 7.ans ans CK- 1 Algebra II with Trigonometr Concepts 3

4 9.ans ans ( ) = 1( + 1) 1. ( 6) = 0( + 3) 13. ( 6) = ( 10) 14. ( + ) = 8( 1) 15. ( 4) = ( + 3), verte is (4, -3) CK- 1 Algebra II with Trigonometr Concepts 4

5 10.3 Circles with Center at the Origin Answers 1.ans ans ans CK- 1 Algebra II with Trigonometr Concepts 5

6 4.ans ans ans = = 36 CK- 1 Algebra II with Trigonometr Concepts 6

7 9. + = = = = no 14. es 15. no 16. a) 1 3 b) 3 c) = = CK- 1 Algebra II with Trigonometr Concepts 7

8 10.4 Circles with Center at (h, k) Answers 1. D. B 3. A 4. C 5.ans ans CK- 1 Algebra II with Trigonometr Concepts 8

9 7.ans ( + 3) + ( + 3) = ( + 7) + ( 6) = ( 8) + ( + 1) = ( + ) + ( + 5) = ( 1) + ( ) = ( 8) + ( + 5) = No, because = ( + ) + ( 4) = 9 ( 9+ 5) + (1 6) 54. CK- 1 Algebra II with Trigonometr Concepts 9

10 10.5 Ellipses with Center at the Origin Answers 1.vertices: (0, ±4), co-vertices: (±3, 0),. vertices: (±5, 0), co-vertices: (0, ±), foci: ( 0, ± 7) ans foci: ( 1,0) ± ans vertices: (±8, 0), co-vertices: (0, ±1), 4. vertices: (±10, 0), co-vertices: (0, ±9), foci: ( ± 3 7,0) ans foci: ( 19,0) ± ans CK- 1 Algebra II with Trigonometr Concepts 10

11 5.vertices: (±7, 0), co-vertices: (0, ±), 6. vertices: (0, ±11), co-vertices: (±3, 0), foci: ( ± 3 5,0) ans foci: ( 1,0) ± ans = = = = = = = 1 79,841 03,85.5 CK- 1 Algebra II with Trigonometr Concepts 11

12 10.6 Ellipses with Center at (h, k) Answers 1. center: (-5, -1), vertices: (-5, -7) and (-5, 5), co-vertices: (0, -1) and (-10, -1), foci: ( 5, 1 ± 11). center: (-, 6), vertices: (-6, 6) and (4, 6), co-vertices: (-, 5) and (-, 7), foci: ( ± 15, 6) 3. center: (-5, -1), vertices: (-5, -7) and (-5, 5), co-vertices: (0, -1) and (-10, -1), foci: ( 5, 1 ± 11) 4. center: (0, 6), vertices: (8, 6) and (-8, 6), co-vertices: (0, 1) and (-0, 11), foci: ( ± 39,6) 5. center: (8, 4), vertices: (8, 1) and (8, 7), co-vertices: (7, 4) and (9, 4), foci: ( 8,4 ± ) 6. center: (-4, -5), vertices: (-4, 4) and (-4, -13), co-vertices: (-, -5) and (-6, -5), foci: ( 4, 5± 77) 7.ans ans CK- 1 Algebra II with Trigonometr Concepts 1

13 9.ans ans ( 3) ( + 3) = ( 5) ( + 3) 1. + = ( 7) ( 4) = ( 3) ( + 3) = ( 3) ( + 3) = CK- 1 Algebra II with Trigonometr Concepts 13

14 10.7 Graphing Hperbolas Centered at the Origin Answers 1.(±3, 0), (±5, 0),.(0, ±5), ( 0, ± 9), 4 =± 3 3.(±9, 0), ( ± 145,0), 5 =± 8 =± 9 4.(±4, 0), ( ±,0), =± 5.(0, ±7), ( 0, ± 74 ), 6.(0, ±3), ( 0, ± 130), 7 =± 5 3 =± 11 7.(0, ±1), ( 0, ± ), =± 8.(±8, 0), ( ± 17,0), 9.(0, ±4), ( 0, ± 17 ), 10.ans =± 1 =± CK- 1 Algebra II with Trigonometr Concepts 14

15 11.ans ans CK- 1 Algebra II with Trigonometr Concepts 15

16 13.ans Answers will var. 15.Foci are ( 34,0) ± and ( 4,0) ±. CK- 1 Algebra II with Trigonometr Concepts 16

17 10.8 Writing the Equation of a Hperbola, Centered at the Origin Answers 1. = = = = = = = = = = 1 or = 1 or = 1 or 36 = = = CK- 1 Algebra II with Trigonometr Concepts 17

18 13. = 1 or = = = CK- 1 Algebra II with Trigonometr Concepts 18

19 10.9 Hperbolas Centered at (h, k) Answers 1.(-5.-1), (0, -1) and (-10, -1), ( 5± 61, 1),.(6, -), (6, ) and (6, -6), ( 6, 17) 3.(3, ), (3, 5) and (3, -1), ( 3,± 58), 4.(0, 6), (8, 6) and (-8, 6), ( ± 68,6), 5.(8, 4), (7, 4) and (9, 4), ( 8 10,4) =± ( + 5) 5 ±, + =± 4( 6) 3 =± ( 3) 5 6 =± 8 ±, 4=± 3( 8) 6.(-5, -4), (-5, -) and (-5, -6), ( 5, 4 ± 85), + 4 =± ( + 5) 9 7.ans ans CK- 1 Algebra II with Trigonometr Concepts 19

20 9.ans ans ( 3 ) ( + 3 ) 11. = ( + 3 ) ( 5 ) 1. = ( + 1 ) ( + 3 ) 13. = ( + 5 ) ( + 4 ) 14. = ( + 5 ) ( + ) 15. = CK- 1 Algebra II with Trigonometr Concepts 0

21 10.10 General Conic Equation Answers 1.Answers will var. ( 3 ) ( + ). = ( 5) = ( 5) ( + 4 ) ( + 3 ) 4. + = ( 5) + = 4 ( 4 ) ( 7 ) 6. + = ( + 5) + ( 5) = ( 1) = ( 7) ( + ) ( + 3 ) 9. = circle, (-1, 1.5) 11.parabola, (1, -9) 1.ellipse, (, 0.5) 13.hperbola, (1.5, -1) 14.parabola, (-5, -3) 15.hperbola, (-, 7) CK- 1 Algebra II with Trigonometr Concepts 1

22 10.11 Classifing Conic Sections Answers 1. circle. hperbola 3. ellipse 4. parabola 5. parabola 6. circle 7. C 8. D 9. A 10. B 11.parabola 1. circle 13.hperbola 14.parabola CK- 1 Algebra II with Trigonometr Concepts

23 15. A = 36π a) ans b) Yes c) A= abπ d) A = 30π, the ellipses are smaller than the circle CK- 1 Algebra II with Trigonometr Concepts 3

24 10.1 Solving Sstems of Lines, Quadratics, and Conics Answers 1. (-1, 8), (-1, -3), (3,.5). (3, 7), -1,.75) 3. (-4, 0), (0, 3.5) 4. (-6.5, 6.5), (6. -3) 5. (1.7, 0.7), (-.3, -3.3) 6. (1.69,.155), (0.71,.645) 7. (±1.076, -.843), (±1.610, ) 8. (0, 10), (, -9) 9. no solution 10. (1, ), (-.67, 4.75) 11. 0, 1,, 3, or , 1,, 3, or One possibilit: intersect. + = 9 and + = 16, the circle are concentric or do not 14. r mr ±, ± 1+ m 1+ m 15. (, ) and (-, -) CK- 1 Algebra II with Trigonometr Concepts 4