Consider the following.

Question

x = e^t - 12
y = e^2t
(a) Eliminate the parameter to find a Cartesian equation of the curve.

Answer 1

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