How to Eliminate the Parameter in a Set of Parametric Equations?

[jcook735]

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

 

[Roni1985]

did you try squaring the x and the y equations ?

 

[jcook735]

well I got x^2 = e^2t + 2 + e^-2t and y^2 = e^2t - 2 + e^-2t but I don't know where to go from there

 

[Roni1985]

if you move the 2's to the other side, your right hand sides are basically equal.

 

[jcook735]

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?

 

[Roni1985]

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?

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, I am not really sure about this.

can you check the answers in the book ?

 

[Dick]

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.