A curve is given by the parametric equations x = (e^t) - 1 and y = e^(2t). a) Eliminate the parameter to find a Cartesian equation of the curve. State the domain and give justification. b) Find the equation of the tangent line to the curve t = ln(4).
Added by George J.
Step 1
Given: \[ x = e^t - 1 \] \[ y = e^{2t} \] From the first equation, we have: \[ e^t = x + 1 \] Substitute this into the second equation: \[ y = (x + 1)^2 \] Therefore, the Cartesian equation of the curve is: \[ \boxed{y = (x + 1)^2} \] ** Show more…
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