# How do you convert the parametric equation to rectangular form x = e^t, y = e^(-t)?

Aug 8, 2016

$y = \frac{1}{x}$

#### Explanation:

Short way...
$x = {e}^{t}$
$y = {e}^{- t} = \frac{1}{e} ^ t = \frac{1}{x}$

Long winded but maybe more interesting way...
$x = {e}^{t} \implies t = \ln x$
$y = {e}^{- t} \implies - t = \ln y$

$\implies \ln x = - \ln y$

$\ln x + \ln y = 0$

$\ln x y = 0$

$x y = {e}^{0} = 1$

$y = \frac{1}{x}$