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Mimi_x3 Group Title

P is the point (2ap,ap^2) on the parabola x^2=4ay. The tangent at P meets the axis of the parabola at T and PN is drawn perpendicular to the axis, meeting it at N. The directrix meets the axis at A. (a) Prove OS=OA

  • 3 years ago
  • 3 years ago

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  1. CrazyEinstein Group Title
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    where is point S?

    • 3 years ago
  2. Mimi_x3 Group Title
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    Um, idk, I think S is the focal length

    • 3 years ago
  3. CrazyEinstein Group Title
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    the definition of the parabola is that the distance between the point P with the focus S is equal to the distance from the point P to the linear directrix. OS=OA is the special situation when P is point O.

    • 3 years ago
  4. CrazyEinstein Group Title
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    Is this what it asks?

    • 3 years ago
  5. Mimi_x3 Group Title
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    idk, i don't understand the question, i just don't understand parametrics xD

    • 3 years ago
  6. Mimi_x3 Group Title
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    Can you help ?

    • 3 years ago
  7. CrazyEinstein Group Title
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    I don't know what the question is asking for.

    • 3 years ago
  8. CrazyEinstein Group Title
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    You must provide more details.

    • 3 years ago
  9. Mimi_x3 Group Title
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    Oh yeah I forgot sorry a) Prove (i) OS=OA (O is vertex, S is the focus)

    • 3 years ago
  10. CrazyEinstein Group Title
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    then i have typed the answer: the definition of the parabola is that the distance between the point P with the focus S is equal to the distance from the point P to the linear directrix. OS=OA is the special situation when P is point O since point O is on the parabola.

    • 3 years ago
  11. Mimi_x3 Group Title
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    Don't you have to solve it or something to prove that OS=OA like finding the equation of tangent

    • 3 years ago
  12. CrazyEinstein Group Title
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    for the question a) OS=OA, I don't think so.

    • 3 years ago
  13. CrazyEinstein Group Title
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    i think you will use it when you are going to solve other questions

    • 3 years ago
  14. Mimi_x3 Group Title
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    Okay, I will draw the diagram that I drew can you check if its correct ?

    • 3 years ago
  15. CrazyEinstein Group Title
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    no problem.

    • 3 years ago
  16. Mimi_x3 Group Title
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    |dw:1318745104246:dw|

    • 3 years ago
  17. Mimi_x3 Group Title
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    Is it right ?

    • 3 years ago
  18. CrazyEinstein Group Title
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    uhh, actually, the directrix is Y=-a, not PN, so point A should be (0,-a) not (2ap, 0) and I don't know why there is another point P on the left side.

    • 3 years ago
  19. Mimi_x3 Group Title
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    hmm..how does it look like then ? In my textbook, in one of the examples there's another P as well so I assume that there's another P in this question idk

    • 3 years ago
  20. CrazyEinstein Group Title
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    for now, you don't need to worry about the other P, just to solve the question will be OK.

    • 3 years ago
  21. Mimi_x3 Group Title
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    Okay, how can I solve it ?

    • 3 years ago
  22. CrazyEinstein Group Title
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    which question? question a is solved through definition of parabola by using the special situation when the point P on the parabola moves to the vertex which is point O.

    • 3 years ago
  23. CrazyEinstein Group Title
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    PS=PN, P is the point on the parabola----the definition

    • 3 years ago
  24. Mimi_x3 Group Title
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    Okay thank you. But one more how can I prove ON=OT, do I use the same definition ?

    • 3 years ago
  25. CrazyEinstein Group Title
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    OK, there is one more mistake which is the axis is X=0 not Y=0 since this parabola is vertical not horizontal. let me draw another diagram just to let you know what it should be. |dw:1318746374530:dw|

    • 3 years ago
  26. Mimi_x3 Group Title
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    wow~ thank you. I drew it totally wrong *sigh* I just don't understand parametrics.

    • 3 years ago
  27. CrazyEinstein Group Title
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    parabola can be vertical or horizontal which depends on the format of the function. The best way to differentiate which is which for me is to learn how to draw it correctly first.

    • 3 years ago
  28. Mimi_x3 Group Title
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    Yeah, I should practice on it. How would I know if its vertical or horizontal ?

    • 3 years ago
  29. CrazyEinstein Group Title
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    X^2=something*Y is vertical, Y^2=something*X is horizontal.

    • 3 years ago
  30. Mimi_x3 Group Title
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    Oh I get it, thank you very much ^_^

    • 3 years ago
  31. CrazyEinstein Group Title
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    You are welcome. I am a PHD student, so heyhey.

    • 3 years ago
  32. Mimi_x3 Group Title
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    Cool~ PHD student. Wonder why you're smart.

    • 3 years ago
  33. CrazyEinstein Group Title
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    Thank you. I am just happy to help people especially in Mathematics because I love it. Don't be afraid of it. It is really cool when you see the essence inside of it.

    • 3 years ago
  34. Mimi_x3 Group Title
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    Lols, I'm afraid it esp parametrics, its like so~ HARD.

    • 3 years ago
  35. Mimi_x3 Group Title
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    of it*

    • 3 years ago
  36. CrazyEinstein Group Title
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    i see. Parametrics is harder but you can consider of them as changeable constants. They are constants but they are changing in different situation.

    • 3 years ago
  37. Mimi_x3 Group Title
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    Oh cool~

    • 3 years ago
  38. CrazyEinstein Group Title
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    back to the question ON=OT, you can not use definition since they are not distances in definition. You need to solve the tangent equation and find out point T. I found it. but they are not equivalent. ON=P^2, OT=(1-2a)*P^2.

    • 3 years ago
  39. Mimi_x3 Group Title
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    Okay, I will work it out.

    • 3 years ago
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