# Thread: Eliminate the Parameter Problem

1. ## Eliminate the Parameter Problem

I have to eliminate the parameter of:

x=e^(t) + e^(-t)
y=6-2t

It has to be Function Y in terms of X.

Everything I do has everything cancel. I can't figure out how to do this. I even tried figuring out what T was in the Y equation, substituting that into the X equation and then getting it in terms of Y. I can't figure it out.

2. ## Hyperbolic

thegame189,

Are you familiar with hyperbolic functions?

--Kevin C.

3. One thing you could do is note that $\displaystyle e^{t}+e^{-t}=2cosh(t)$

Therefore, $\displaystyle x=2cosh(t), \;\ t=cosh^{-1}(\frac{x}{2})$

Sub into y and get $\displaystyle y=6-2cosh^{-1}(\frac{x}{2})$

4. Can someone check the answers I got for these?

Find the EXACT length of C. I got:

L = e^(3) - e^(-3)

Find the EXACT area of the surface obtained by rotating C about the x-axis.
I got:

A = 2*Pi*[4e^3 - 1]

I used the formula L = sqrt of [(dx^2) + (dy^2)], which then factored factored into [e^(t) + e^(-t)]... I then put the 3 and 0 in to get the Length. Any mistakes?

For Area, I did the same thing but then multiplied it by 2Pi*Y, which is 2Pi*(6-2t)... I then FOILed and had to integrate: 6e^(t) -te^(t) + 6e^(-t) -te^(-t). I got: 6e^(t) - te^(t) + e^(t) - 6e^(-t) + te^(-t) + te^(-t) and evaluated it from 0 to 3. I got: [6e^3 - 3e^3 + e^3 - 6e^(-3) + 6e^(-3). My final was: [2Pi(4e^3 - 1)]

See any mistakes?