Curves defined by parameteric equations

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

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  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

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