question
How to graph the parametric equation: $y=e^{-t}$ and $x=e^{t}$
I preferable would like to cancel out the t's on both sides so then I instinctively ln both sides but that gives me ln(x)=t and ln(y)=-t to devolve into me adding the two equations to finally devolve into the following:
x=y which doesn't seem like the real solution/equation to the problem
Best Answer
$y = e^{-t} \implies y = \frac{1}{e^t} = \frac{1}{x} $ as $x = e^t$. So the equation is is $y = \frac{1}{x}$.
The way you have solved it (by taking ln) gives $ln(x) +ln(y) =0 \implies ln(xy) = 0 $ or $xy =1$.