1. ## Parametric equations

Hello,

I have this problem..

x = et - 4
y = e2t

Eliminate the parameter and find the Cartesian equation of the curve.

y = ?

So far I have gotten
y = exp(8) * exp(2 ln x)
but It says I am wrong. Can anyone else verify?

2. Could you clarify whether that eqaution is x=exp(x) - 4
or x=exp(x-4)

3. Originally Posted by aznstyles408
Hello,

I have this problem..

x = et - 4
y = e2t

Eliminate the parameter and find the Cartesian equation of the curve.

y = ?

So far I have gotten
y = exp(8) * exp(2 ln x)
but It says I am wrong. Can anyone else verify?

$\displaystyle x = e^t - 4 \Rightarrow x + 4 = e^t \Rightarrow (x + 4)^2 = e^{2t}$ .... (1)

$\displaystyle y = e^{2t}$ .... (2)

Add equations (1) and (2) together.

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$\displaystyle x = e^{t - 4} = e^t e^{-4} \Rightarrow e^4 x = e^t \Rightarrow e^8 x^2 = e^{2t}$ .... (1)

$\displaystyle y = e^{2t}$ .... (2)

Add equations (1) and (2) together.