Finding the Cartesian equation for x = e^t, y = e^-t

[Caldus]

Another question...

If I were given these equations:

x = e^t
y = e^-t

Then I have to find the cartesian product for this parametric curve and then I have to sketch the graph of the curve. So here's the cartesian product I came up with:

Solve for t in y, so:

y = e^-t
ln y = ln e^-t
ln y = -t
t = - ln y

Then plug into the x part:

x = e^-ln y

Is that part correct?

I have no idea how to graph this...

Help appreciated.

 

[Hurkyl]

Do you know any identities applicable to it?

 

[matt grime]

Simple method: u^{-r}= 1/u^r
slightly longer metheod, try multiplying x and y together!

or:

-log(p) = log(1/p)
e^log(w)=w

any of those help?