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# 1004 ch 10 day 4

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• ### 1004 ch 10 day 4

1. 1. 10.2 The Ellipse Day TwoGalatians 2:20 "I have been cruciﬁed with Christ. It is nolonger I who live, but Christ who lives in me. And the life Inow live in the ﬂesh I live by faith in the Son of God, wholoved me and gave himself for me."
2. 2. The eccentricity of an ellipse is how much itvaries from being a circle ... it is the ratio ofc to a c 2 2 e= where c = a − b a
3. 3. The eccentricity of an ellipse is how much itvaries from being a circle ... it is the ratio ofc to a c 2 2 e= where c = a − b a 0 < e <1
4. 4. The eccentricity of an ellipse is how much itvaries from being a circle ... it is the ratio ofc to a c 2 2 e= where c = a − b a 0 < e <1 e close to 0 is very circular e close to 1 is really stretched out
5. 5. 1. The vertices of an ellipse are ( ± 6,0 ) and the foci are ( ± 4,0 ) . Find its equation.
6. 6. 1. The vertices of an ellipse are ( ± 6,0 ) and the foci are ( ± 4,0 ) . Find its equation. 2 2 2 a=6 c=4 c = a −b
7. 7. 1. The vertices of an ellipse are ( ± 6,0 ) and the foci are ( ± 4,0 ) . Find its equation. 2 2 2 a=6 c=4 c = a −b 2 2 2 4 = 6 −b
8. 8. 1. The vertices of an ellipse are ( ± 6,0 ) and the foci are ( ± 4,0 ) . Find its equation. 2 2 2 a=6 c=4 c = a −b 2 2 2 4 = 6 −b 2 2 2 b =6 −4
9. 9. 1. The vertices of an ellipse are ( ± 6,0 ) and the foci are ( ± 4,0 ) . Find its equation. 2 2 2 a=6 c=4 c = a −b 2 2 2 4 = 6 −b 2 2 2 b =6 −4 2 b = 20
10. 10. 1. The vertices of an ellipse are ( ± 6,0 ) and the foci are ( ± 4,0 ) . Find its equation. 2 2 2 a=6 c=4 c = a −b 2 2 2 4 = 6 −b 2 2 2 b =6 −4 2 b = 20 2 2 x y + =1 36 20
11. 11. 2. Find the foci of the ellipse 9x + 4y = 36 2 2
12. 12. 2. Find the foci of the ellipse 9x + 4y = 36 2 2 2 2 x y + =1 4 9
13. 13. 2. Find the foci of the ellipse 9x + 4y = 36 2 2 2 2 x y + =1 4 9 2 2 2 c = a −b
14. 14. 2. Find the foci of the ellipse 9x + 4y = 36 2 2 2 2 x y + =1 4 9 2 2 2 c = a −b 2 c = 9−4 = 5
15. 15. 2. Find the foci of the ellipse 9x + 4y = 36 2 2 2 2 x y + =1 4 9 2 2 2 c = a −b 2 c = 9−4 = 5 c=± 5
16. 16. 2. Find the foci of the ellipse 9x + 4y = 36 2 2 2 2 x y + =1 4 9 2 2 2 c = a −b 2 c = 9−4 = 5 c=± 5 ( F 0, ± 5 )
17. 17. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5
18. 18. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5c = 20
19. 19. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5c = 20 ce= a
20. 20. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5c = 20 ce= a4 20 =5 a
21. 21. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5c = 20 ce= a4 20 =5 aa = 25
22. 22. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5 c = 20 c e= a4 20 =5 aa = 25 2a = 625
23. 23. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5 2 c = 20 c = 400 c e= a4 20 =5 aa = 25 2a = 625
24. 24. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5 2 c = 20 c = 400 c e= 2 2 c = a −b 2 a4 20 =5 aa = 25 2a = 625
25. 25. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5 2 c = 20 c = 400 c e= 2 2 c = a −b 2 a 2 2 24 20 b =a −c =5 aa = 25 2a = 625
26. 26. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5 2 c = 20 c = 400 c e= 2 2 c = a −b 2 a 2 2 24 20 b =a −c = 25 a b = 625 − 400a = 25 2a = 625
27. 27. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e = 5 2 c = 20 c = 400 c e= 2 2 c = a −b 2 a 2 2 24 20 b =a −c = 25 a b = 625 − 400a = 25 2 b = 225 2a = 625
28. 28. 3. Find the equation of the ellipse with foci 4 ( 0, ± 20 ) and eccentricity e =5 2 c = 20 c = 400 c e= 2 2 c = a −b 2 a 2 2 24 20 b =a −c = 25 a b = 625 − 400a = 25 2 b = 225 2a = 625 2 x y 2 + =1 225 625
29. 29. 4. Find the vertices, foci and eccentricity of the ellipse, 4x + y = 16 . Determine the 2 2 lengths of the major and minor axes and sketch the graph.
30. 30. 4. Find the vertices, foci and eccentricity of the ellipse, 4x + y = 16 . Determine the 2 2 lengths of the major and minor axes and sketch the graph. 2 2 x y + =1 4 16
31. 31. 4. Find the vertices, foci and eccentricity of the ellipse, 4x + y = 16 . Determine the 2 2 lengths of the major and minor axes and sketch the graph. 2 2 x y + =1 4 16 a=4 b=2 2 c = 16 − 4 = 12 c=2 3
32. 32. 4. Find the vertices, foci and eccentricity of the ellipse, 4x + y = 16 . Determine the 2 2 lengths of the major and minor axes and sketch the graph. x2 y 2 vertices : ( 0, ± 4 ) + =1 4 16 foci : ( 0, ± 2 3 ) a=4 b=2 3 e: 2 c = 16 − 4 = 12 2 major : 8 c=2 3 minor : 4 sketch of graph on next slide
33. 33. HW #4“Of those to whom much is given, much is required.” John F. Kennedy