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# 1006 ch 10 day 6

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• ### 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