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How do you go about solving this problem?

For each plane curve given below, find a rectangular equation. State the appropritate interval for $x$ and $y$.

$x(t) = e^{5t}$, $y(t) = e^t$, $t \in (-\infty, \infty)$.

Which is the correct rectangular equation?

(a) $x = \frac 1{y^5}$

(b) $y = x^5$

(c) $y = \frac 1{x^5}$

(d) $x = y^5$.

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    $\begingroup$ $ x(t) = (e^t)^5 $ $\endgroup$ – Santosh Linkha Jun 13 '12 at 8:36
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Since you are given alternatives, you can simply plug in and check:

(A) $x = 1/y^5$ gives $e^{5t} = 1/(e^t)^5$, which is not true. So (A) is wrong.

Etc.

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