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Angle of Ellipse?

  1. Jul 12, 2011 #1
    Hi everyone,

    As I wasn't able to find it within my calculus book, can someone master here please tell me is there any way to find the angle of ellipse?

    Thank you

    Huygen
     
  2. jcsd
  3. Jul 12, 2011 #2

    phinds

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    What does that mean to you, "the angle of an ellipse" ? Your question is too vague to answer.

    If you mean the tangent at any point on the ellipse, then that's trivial.
     
  4. Jul 12, 2011 #3
    What information do you have about the ellipse? Maybe you have its equation and you want to know the angle of the axis?
     
  5. Jul 12, 2011 #4
    Generally, the "zero degree" point on an ellipse is taken as the periapse, which is the point on the ellipse closest to one of the two focus points. The angular position is then generally referred to as the "True Anomaly", which is the angle between two lines, the first being from the focus to the periapse; the second being from that same focus to the point on the ellipse in question.

    hth
     
  6. Jul 13, 2011 #5
    Forget my previous question.

    Now, I would like to ask again, if possible, can someone here please tell me how to find the center of ellipse in a given quadrilateral, which the ellipse is lying inside the quadrilateral and tangent to the four sides of the quadrilateral?
     
  7. Jul 13, 2011 #6

    phinds

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    You have to specify exactly the characteristics of the quadrilateral. For example if the ellipse is inside a rectangle AND their axes coincide, then they have the same center.
     
  8. Jul 13, 2011 #7
    What about this (please see attached image)?

    This ellipse looks tangent to all of the three triangle edges, but it seems the ellipse center and the triangle center is not coinciding?
     

    Attached Files:

  9. Jul 13, 2011 #8
    He said "rectangle", not "triangle".

    As to your original question, I don't have an answer, but I'll point out that it is not always possible to construct an ellipse tangent to all four sides of a quadrilateral.
     
  10. Jul 13, 2011 #9

    phinds

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    Fellow, you are really not doing well here. First you post a question with insufficient information for there to be an answer then you abandon it. Then you post a question about quadrilaters but don't specify ANY of their characteristics, then you respond to my quadrilateral answer with a question that is NOT even a quatrilateral, it a tri-lateral (more commonly called a triangle).

    Try asking a meaningful question with enough information for there to be a meaningful answer and perhaps someone will be able to help you. I'm not going to try any further.
     
  11. Jul 13, 2011 #10
    I am sorry...

    Why I replace the quadrilateral with the triangle in my previous question is, because I can not find the center of the quadrilateral by drawing compared to the regular rectangle which is relative simple to find its center by drawing.

    Also, what properties of the quadrilateral or tri-lateral is required?
     
  12. Jul 14, 2011 #11
    Well, for instance, if you could give the coordinates of all four vertices that should be enough information to uniquely determine the answer (if there is one). However, this is an unusual enough question that I doubt anyone will know the answer off the top of their heads. It also looks to me like it would take a fair amount of work to solve. So, you may be stuck with figuring it out yourself.

    May I ask why you need to know this? Do you need the answer for a completely general tetralateral? If, for instance, you were really only interested in trapezoids, it would become a lot easier.
     
  13. Jul 14, 2011 #12
    OK, let the four cartesian point of the vertex of the quadrilateral be A(0,0), B(2,0), C(2,1), D(-1,2).

    How can I find the center point of an ellipse and plot it inside above quadrilateral which tangent to the four edge of it (the quadrilateral)?
     
  14. Jul 14, 2011 #13
    May I ask why you need to know this? Do you need the answer for a completely general tetralateral? If, for instance, you were really only interested in trapezoids, it would become a lot easier.
     
  15. Jul 14, 2011 #14
    I would like to know more about an ellipse property.

    Does tetralateral is similar with quadrilateral, more or less?

    If yes, then the answer is yes.

    Very well then, trapezoid is OK.

    Just use the property (cartesian point) I post on my previous answer.
     
  16. Jul 14, 2011 #15
    So, just curiosity? In that case, I think you'll get more out of it if you figure it out yourself.

    You do realize, as I mentioned earlier, that answering your question would be a great deal of work for someone? It seems most appropriate that the someone be you.

    Yes -- sorry. That's what I meant.

    The points in your previous post do not describe a trapezoid.
     
  17. Jul 14, 2011 #16
    OK, let the cartesian point of the trapezoid be A(0,0), B(3,0), C(3,1), D(1,1).
     
  18. Jul 15, 2011 #17
    Good. You have a way to unambiguously define a quadrilateral, and you have chosen one. Next question I would ask: how do you define a specific ellipse?
     
  19. Jul 15, 2011 #18
    OK.

    What do you ask me back as I ask it in this discussion?

    I don't know.
     
  20. Jul 15, 2011 #19
    I already explained why. You are asking for a whole lot of work to be done. You have given no reason for anyone to do this work, except to satisfy your curiosity. Therefore, it seems clear to me that YOU are the person who should be doing most of the work.

    Well THINK about it, for Pete's sake. Have an idea or two!
     
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