Chapter 10             Conic Sections (Be sure you have printed out your Conics Help Sheet)Revelation 1:7 "Behold, he is c...
Conic Sections are the curves we obtain whenintersecting a plane with a double-cone atvarious angles.                 use ...
Conic Sections are the curves we obtain whenintersecting a plane with a double-cone atvarious angles.                 use ...
10.1 The Parabola
10.1 The ParabolaAnother way to define the     parabola is this:A Parabola is the set ofpoints in the planeequidistant from...
10.1 The ParabolaAnother way to define the     parabola is this:A Parabola is the set ofpoints in the planeequidistant from...
axis of symmetry   vertexThe parts of a parabola
Consider ... the vertex at the Origin
Consider ... the vertex at the Origin
Consider ... the vertex at the Origin                                        FP = PT
Consider ... the vertex at the Origin                                         FP = PT                                     ...
Consider ... the vertex at the Origin                                          FP = PT                                    ...
Consider ... the vertex at the Origin                                          FP = PT                                    ...
Consider ... the vertex at the Origin                                          FP = PT                                    ...
Consider ... the vertex at the Origin                                          FP = PT                                    ...
Consider ... the vertex at the Origin                                           FP = PT                                   ...
Consider ... the vertex at the Origin                                           FP = PT                                   ...
If we take the inverse (interchange x and y) theparabola is reflected over the y=x line ...
If we take the inverse (interchange x and y) theparabola is reflected over the y=x line ...
If we take the inverse (interchange x and y) theparabola is reflected over the y=x line ...                                ...
If we take the inverse (interchange x and y) theparabola is reflected over the y=x line ...                                ...
1. Find the equation of the parabola with   vertex V ( 0, 0 ) and focus F ( 0, − 8 ) .
1. Find the equation of the parabola with   vertex V ( 0, 0 ) and focus F ( 0, − 8 ) .                  2                 ...
1. Find the equation of the parabola with   vertex V ( 0, 0 ) and focus F ( 0, − 8 ) .                  2                 ...
1. Find the equation of the parabola with   vertex V ( 0, 0 ) and focus F ( 0, − 8 ) .                  2                 ...
2. Find the focus and directrix of the parabola           2   y = −5x
2. Find the focus and directrix of the parabola           2   y = −5x                2               x = 4 py
2. Find the focus and directrix of the parabola           2   y = −5x                2               x = 4 py             ...
2. Find the focus and directrix of the parabola           2   y = −5x                2               x = 4 py             ...
2. Find the focus and directrix of the parabola           2   y = −5x                2               x = 4 py             ...
2. Find the focus and directrix of the parabola           2   y = −5x                       2                   x = 4 py  ...
3. Find the focus and directrix of the parabola         2   2x + y = 0
3. Find the focus and directrix of the parabola         2   2x + y = 0                2               y = −2x
3. Find the focus and directrix of the parabola         2   2x + y = 0                2               y = −2x             ...
3. Find the focus and directrix of the parabola         2   2x + y = 0                2               y = −2x             ...
3. Find the focus and directrix of the parabola         2   2x + y = 0                      2                  y = −2x    ...
4. Find the focus, directrix and focal diameter of       4 2   y= x       9
4. Find the focus, directrix and focal diameter of       4 2   y= x       9                  9             4p =           ...
4. Find the focus, directrix and focal diameter of       4 2   y= x       9                  9             4p =         th...
4. Find the focus, directrix and focal diameter of       4 2   y= x       9                  9             4p =         th...
4. Find the focus, directrix and focal diameter of       4 2   y= x       9                   9              4p =         ...
When you are asked to graph these ...use your calculator and then put them on graph paper.                     HW #1“Coura...
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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

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