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# 1001 ch 10 day 1

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• ### 1001 ch 10 day 1

1. 1. Chapter 10 Conic Sections (Be sure you have printed out your Conics Help Sheet)Revelation 1:7 "Behold, he is coming with the clouds, andevery eye will see him, even those who pierced him, and alltribes of the earth will wail on account of him. Even so. Amen."
2. 2. Conic Sections are the curves we obtain whenintersecting a plane with a double-cone atvarious angles. use K on keyboard to Pause/Play
3. 3. Conic Sections are the curves we obtain whenintersecting a plane with a double-cone atvarious angles. use K on keyboard to Pause/Play
4. 4. 10.1 The Parabola
5. 5. 10.1 The ParabolaAnother way to deﬁne the parabola is this:A Parabola is the set ofpoints in the planeequidistant from a ﬁxedpoint, F (the Focus), anda ﬁxed line, l (theDirectrix).
6. 6. 10.1 The ParabolaAnother way to deﬁne the parabola is this:A Parabola is the set ofpoints in the planeequidistant from a ﬁxedpoint, F (the Focus), anda ﬁxed line, l (theDirectrix).
7. 7. axis of symmetry vertexThe parts of a parabola
8. 8. Consider ... the vertex at the Origin
9. 9. Consider ... the vertex at the Origin
10. 10. Consider ... the vertex at the Origin FP = PT
11. 11. Consider ... the vertex at the Origin FP = PT 2 2 ( x − 0) + ( y − p) = y+ p
12. 12. Consider ... the vertex at the Origin FP = PT 2 2 ( x − 0) + ( y − p) = y+ p 2 2 2 2 2 x + y − 2 py + p = y + 2 py + p
13. 13. Consider ... the vertex at the Origin FP = PT 2 2 ( x − 0) + ( y − p) = y+ p 2 2 2 2 2 x + y − 2 py + p = y + 2 py + p 2 x = 4 py
14. 14. Consider ... the vertex at the Origin FP = PT 2 2 ( x − 0) + ( y − p) = y+ p 2 2 2 2 2 x + y − 2 py + p = y + 2 py + p 2 x = 4 py vertex : ( 0, 0 )
15. 15. Consider ... the vertex at the Origin FP = PT 2 2 ( x − 0) + ( y − p) = y+ p 2 2 2 2 2 x + y − 2 py + p = y + 2 py + p 2 x = 4 py vertex : ( 0, 0 ) focus : ( 0, p )
16. 16. Consider ... the vertex at the Origin FP = PT 2 2 ( x − 0) + ( y − p) = y+ p 2 2 2 2 2 x + y − 2 py + p = y + 2 py + p 2 x = 4 py vertex : ( 0, 0 ) focus : ( 0, p ) directrix : y = − p
17. 17. Consider ... the vertex at the Origin FP = PT 2 2 ( x − 0) + ( y − p) = y+ p 2 2 2 2 2 x + y − 2 py + p = y + 2 py + p 2 x = 4 py vertex : ( 0, 0 ) focus : ( 0, p ) directrix : y = − p p > 0, opens up p < 0, opens down
18. 18. If we take the inverse (interchange x and y) theparabola is reﬂected over the y=x line ...
19. 19. If we take the inverse (interchange x and y) theparabola is reﬂected over the y=x line ...
20. 20. If we take the inverse (interchange x and y) theparabola is reﬂected over the y=x line ... 2 y = 4 px vertex : ( 0, 0 ) focus : ( p, 0 ) directrix : x = − p p > 0, opens right p < 0, opens left
21. 21. If we take the inverse (interchange x and y) theparabola is reﬂected over the y=x line ... 2 y = 4 px vertex : ( 0, 0 ) focus : ( p, 0 ) latus rectum directrix : x = − p p > 0, opens right p < 0, opens leftThe Latus Rectum (also called the focal diameter) is thesegment with endpoints on the parabola, is perpendicularto the axis of symmetry and contains the focus point.Its length is 4 p .
22. 22. 1. Find the equation of the parabola with vertex V ( 0, 0 ) and focus F ( 0, − 8 ) .
23. 23. 1. Find the equation of the parabola with vertex V ( 0, 0 ) and focus F ( 0, − 8 ) . 2 x = 4 py
24. 24. 1. Find the equation of the parabola with vertex V ( 0, 0 ) and focus F ( 0, − 8 ) . 2 x = 4 py p = −8
25. 25. 1. Find the equation of the parabola with vertex V ( 0, 0 ) and focus F ( 0, − 8 ) . 2 x = 4 py p = −8 2 x = −32y
26. 26. 2. Find the focus and directrix of the parabola 2 y = −5x
27. 27. 2. Find the focus and directrix of the parabola 2 y = −5x 2 x = 4 py
28. 28. 2. Find the focus and directrix of the parabola 2 y = −5x 2 x = 4 py 2 1 x =− y 5
29. 29. 2. Find the focus and directrix of the parabola 2 y = −5x 2 x = 4 py 2 1 x =− y 5 1 ∴ 4p = − 5
30. 30. 2. Find the focus and directrix of the parabola 2 y = −5x 2 x = 4 py 2 1 x =− y 5 1 ∴ 4p = − 5 1 p=− 20
31. 31. 2. Find the focus and directrix of the parabola 2 y = −5x 2 x = 4 py 12 x =− y 5 1 ∴ 4p = − 5 1 p=− 20 ⎛ 1 ⎞ 1 F ⎜ 0, − ⎟ dir : y = ⎝ 20 ⎠ 20
32. 32. 3. Find the focus and directrix of the parabola 2 2x + y = 0
33. 33. 3. Find the focus and directrix of the parabola 2 2x + y = 0 2 y = −2x
34. 34. 3. Find the focus and directrix of the parabola 2 2x + y = 0 2 y = −2x 4 p = −2
35. 35. 3. Find the focus and directrix of the parabola 2 2x + y = 0 2 y = −2x 4 p = −2 1 p=− 2
36. 36. 3. Find the focus and directrix of the parabola 2 2x + y = 0 2 y = −2x 4 p = −2 1 p=− 2 ⎛ 1 ⎞ 1 F ⎜ − , 0 ⎟ dir : x = ⎝ 2 ⎠ 2
37. 37. 4. Find the focus, directrix and focal diameter of 4 2 y= x 9
38. 38. 4. Find the focus, directrix and focal diameter of 4 2 y= x 9 9 4p = 4
39. 39. 4. Find the focus, directrix and focal diameter of 4 2 y= x 9 9 4p = this is the focal diameter 4
40. 40. 4. Find the focus, directrix and focal diameter of 4 2 y= x 9 9 4p = this is the focal diameter 4 9 p= 16
41. 41. 4. Find the focus, directrix and focal diameter of 4 2 y= x 9 9 4p = this is the focal diameter 4 9 p= 16 ⎛ 9 ⎞ 9 9 F ⎜ 0, ⎟ dir : y = − foc. dia : ⎝ 16 ⎠ 16 4
42. 42. When you are asked to graph these ...use your calculator and then put them on graph paper. HW #1“Courage is the ﬁrst of human qualities because it isthe quality which guarantees all others.” Winston Churchill