10.3 HyperbolasJohn 17:3 "And this is eternal life, that they know you theonly true God, and Jesus Christ whom you have se...
Another way to definethe hyperbola is this:A Hyperbola is the setof points in the plane,the difference of whosedistances fr...
Another way to definethe hyperbola is this:A Hyperbola is the setof points in the plane,the difference of whosedistances fr...
F2   F1
Vertex   Vertex F2       F1
Central BoxVertex                 Vertex F2                     F1
Central BoxVertex                 Vertex F2                     F1         Asymptotes
Central Box              Vertex                 Vertex               F2                     F1                       Asymp...
To derive the equation for a hyperbola ... start with               PF2 − PF1 = 2a
To derive the equation for a hyperbola ... start with               PF2 − PF1 = 2aIt is very similar to what we did with t...
To derive the equation for a hyperbola ... start with               PF2 − PF1 = 2aIt is very similar to what we did with t...
A bit more detail ...
A bit more detail ...                        V1V2 :Transverse Axis                        B1 B2 :Conjugate Axis
A bit more detail ...                                 V1V2 :Transverse Axis                                 B1 B2 :Conjuga...
A bit more detail ...                                          V1V2 :Transverse Axis                                      ...
To sketch a hyperbola:
To sketch a hyperbola:  1. Draw the central box
To sketch a hyperbola:  1. Draw the central box  2. Draw in the asymptotes
To sketch a hyperbola:  1. Draw the central box  2. Draw in the asymptotes  3. Plot the vertices and foci
To sketch a hyperbola:  1. Draw the central box  2. Draw in the asymptotes  3. Plot the vertices and foci  4. Draw the hyp...
2   21. Discuss and graph:   x   y                          −   =1                        16 25
2       21. Discuss and graph:       x   y                              −   =1                            16 25           ...
2        21. Discuss and graph:             x   y                                    −   =1                               ...
2. Discuss and graph:     2   2                        4x − y + 4 = 0
2. Discuss and graph:         2   2                            4x − y + 4 = 0                 2      2               4x − ...
2. Discuss and graph:         2   2                            4x − y + 4 = 0                 2      2               4x − ...
2. Discuss and graph:            2       2                            4x − y + 4 = 0                 2      2             ...
2. Discuss and graph:                     2       2                                     4x − y + 4 = 0                    ...
HW #6“The difference between the possible and the impossiblelies in a man’s determination.”                     Tommy Laso...
1006 ch 10 day 6
1006 ch 10 day 6
Upcoming SlideShare
Loading in …5
×

1006 ch 10 day 6

204 views

Published on

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
204
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • \n
  • 1006 ch 10 day 6

    1. 1. 10.3 HyperbolasJohn 17:3 "And this is eternal life, that they know you theonly true God, and Jesus Christ whom you have sent."
    2. 2. Another way to definethe hyperbola is this:A Hyperbola is the setof points in the plane,the difference of whosedistances from twofixed points (the Foci),is a constant. use K on keyboard to Pause/Play
    3. 3. Another way to definethe hyperbola is this:A Hyperbola is the setof points in the plane,the difference of whosedistances from twofixed points (the Foci),is a constant. use K on keyboard to Pause/Play
    4. 4. F2 F1
    5. 5. Vertex Vertex F2 F1
    6. 6. Central BoxVertex Vertex F2 F1
    7. 7. Central BoxVertex Vertex F2 F1 Asymptotes
    8. 8. Central Box Vertex Vertex F2 F1 AsymptotesThe segment joining V1 and V2 is the Transverse Axis.
    9. 9. To derive the equation for a hyperbola ... start with PF2 − PF1 = 2a
    10. 10. To derive the equation for a hyperbola ... start with PF2 − PF1 = 2aIt is very similar to what we did with the ellipse, so wewon’t go through all of that again. The equation is:
    11. 11. To derive the equation for a hyperbola ... start with PF2 − PF1 = 2aIt is very similar to what we did with the ellipse, so wewon’t go through all of that again. The equation is: 2 2 x y 2 − 2 =1 a b
    12. 12. A bit more detail ...
    13. 13. A bit more detail ... V1V2 :Transverse Axis B1 B2 :Conjugate Axis
    14. 14. A bit more detail ... V1V2 :Transverse Axis B1 B2 :Conjugate Axis 2 2x y 2 − 2 = 1 opens left − righta b
    15. 15. A bit more detail ... V1V2 :Transverse Axis B1 B2 :Conjugate Axis 2 2 2 2x y y x 2 − 2 = 1 opens left − right 2 − 2 = 1 opens up − downa b a b
    16. 16. To sketch a hyperbola:
    17. 17. To sketch a hyperbola: 1. Draw the central box
    18. 18. To sketch a hyperbola: 1. Draw the central box 2. Draw in the asymptotes
    19. 19. To sketch a hyperbola: 1. Draw the central box 2. Draw in the asymptotes 3. Plot the vertices and foci
    20. 20. To sketch a hyperbola: 1. Draw the central box 2. Draw in the asymptotes 3. Plot the vertices and foci 4. Draw the hyperbola
    21. 21. 2 21. Discuss and graph: x y − =1 16 25
    22. 22. 2 21. Discuss and graph: x y − =1 16 25 2 2 2 a=4 b=5 c = a +b c = 41 ≈ 6.4
    23. 23. 2 21. Discuss and graph: x y − =1 16 25 2 2 2 a=4 b=5 c = a +b c = 41 ≈ 6.4 Vert. : ( ± 4,0 ) Foci : ( ± 6.4,0 ) TA : 8 CA : 10 5 Asy. : y = ± x 4
    24. 24. 2. Discuss and graph: 2 2 4x − y + 4 = 0
    25. 25. 2. Discuss and graph: 2 2 4x − y + 4 = 0 2 2 4x − y = −4
    26. 26. 2. Discuss and graph: 2 2 4x − y + 4 = 0 2 2 4x − y = −4 2 2 y x − =1 4 1
    27. 27. 2. Discuss and graph: 2 2 4x − y + 4 = 0 2 2 4x − y = −4 2 2 y x − =1 4 1 2 2 2 a=2 b =1 c = a +b c = 5 ≈ 2.2
    28. 28. 2. Discuss and graph: 2 2 4x − y + 4 = 0 2 2 4x − y = −4 2 2 y x − =1 4 1 2 2 2 a=2 b =1 c = a +b c = 5 ≈ 2.2 Vert. : ( 0, ± 2 ) Foci : ( 0, ± 2.2 ) TA : 4 CA : 2 x Asy. : y = ± 2
    29. 29. HW #6“The difference between the possible and the impossiblelies in a man’s determination.” Tommy Lasorda

    ×