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

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Answer 1 · 2016-08-08T12:38:21

#y = 1/x#

Short way...
#x = e^t#
#y = e^(-t) = 1/e^t = 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 xy = 0#

#xy = e^0 = 1#

#y = 1/x#