# Curves defined by parameteric equations

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

• Curves defined by parameteric equations -

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

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