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Equation of the path of the particle

  1. Jun 22, 2013 #1
    1. The problem statement, all variables and given/known data
    The x and y coordinates of a particle moving in the x-y plane are [tex]x=8sin(t)[/tex] and [tex]y=6cos(t)[/tex]. What is the equation of the path of the particle?


    2. Relevant equations
    [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
    [tex]y-y_1=m(x-x_1)[/tex]

    3. The attempt at a solution
    I am stuck on how to approach this problem.
    I drew a picture:
    7jw9usI.png . Can I use one point as the origin, (0,0) and the second point as (8sint, 6cost) and use the equation of a line to find the 'path' of the particule? I am confused if the path of the particule means the equation of the line?

    Any tips and hints would be great. Thanks!
     
  2. jcsd
  3. Jun 22, 2013 #2

    tiny-tim

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    hi skybox! :smile:
    no, the path of the particle means the curve joining all the points (8sint, 6cost) :wink:

    (if you're still stuck, come back for a hint)
     
  4. Jun 22, 2013 #3
    Thanks tiny-tim. After some research, looks like this is a parametric equation. Since it has cosines and sines, it will most likely be a circle or ellipse from [tex]0<=x<=2\pi[/tex].

    I will try to solve this and post the solution when done. Thanks again!
     
  5. Jun 22, 2013 #4
    I was able to solve it! Attached is the solution (as an image I did in Word) if anyone is interested.
     

    Attached Files:

  6. Jun 23, 2013 #5

    tiny-tim

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    me! me! i'm interested! :smile:

    yes, nicely done :wink:

    (btw, for a lot of purposes, the form x2/a2 + y2/b2 = 1 is preferred, so you could have stopped there)
     
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