Why does $x=e^t+2e^{-t},y=e^t-2e^{-t}$ plot to a straight line? This parametrization satisfies $x^2-y^2=8$, so I was expecting a hyperbola. But what I got was a straight line. Why though?
https://www.wolframalpha.com/input/?i=parametric+plot+%28e%5Et%2B2e%5E%28-t%29%2Ce%5Et-2e%5E%28-t%29%29
EDIT- I tried a different range for $t$ and the point (8,0) isn't even on the line that gets plotted 

Try to make the plot for $t$ between for example -3 and 3, the you should see it. Also, the point $(\sqrt 8,0)$ should be on there, not $(8,0)$. 
Regarding the comments, it does not give a straight line, since the constant term depends on $t$, which varies. However, the reason why it looks like a straight line is that for 'large' $t > 0$ we have that $x \approx e^t$ and $y \approx e^t$, so that $y \approx x$. A similar thing happens for large negative $t$. 
