Curves defined by parameteric equations
posted by Mike .
Consider the following.
x = e^t  12
y = e^2t
(a) Eliminate the parameter to find a Cartesian equation of the curve.

from x = e^t  12
e^t = x+12
t = ln(x+12)
form y = e^2t
2t = lny
t = (lny)/2
so (ln y)/2 = ln(x+12)
lny = 2ln(x+12)
lny = ln(x+12)^2
y = (x+12)^2