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Eliminating the parameter

  1. Feb 24, 2010 #1
    Express the set of parametric equations x = E^t + e^-t and y = e^t - e^-t without using the parameter t.


    I really have no idea how to do this one. I tried substituting, and it just turned into a jumbled mess of nothing. Please help
     
  2. jcsd
  3. Feb 24, 2010 #2
    did you try squaring the x and the y equations ?
     
  4. Feb 24, 2010 #3
    well I got x^2 = e^2t + 2 + e^-2t and y^2 = e^2t - 2 + e^-2t but I dont know where to go from there
     
  5. Feb 24, 2010 #4
    if you move the 2's to the other side, your right hand sides are basically equal.
     
  6. Feb 24, 2010 #5
    OH!!! Thanks! So if I understand correctly, ill move the twos over and get the right sides to be the same and x^2 - 2 and y^2 +2. Then I should set these two equal to each other and find y, which comes out to be (plus or minus) the square root of x^2 - 4?
     
  7. Feb 24, 2010 #6
    I think you need to take only the 'plus', because if I'm not mistaken, Y can't be negative according to the parametric equations.
    So the range is Y=>0.
    I am not really sure about this.
    even if 't' is negative (do you have the domain of t ?), these equations can never be negative (neither the X nor the Y).
    again, im not really sure about this.

    can you check the answers in the book ?
     
  8. Feb 24, 2010 #7

    Dick

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    Yes, x^2-y^2=4. If that's what you mean. There's no need to solve for x or y is you just want to eliminate the parameter.
     
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