Final answer:
To eliminate the parameter and find a Cartesian equation of the curve, solve equation (a) for t in terms of x and substitute it into equation (b) to get y = (x + 9)^2.
Step-by-step explanation:
To eliminate the parameter and find a Cartesian equation of the curve, we can first solve equation (a) for t in terms of x and substitute it into equation (b).
From equation (a), x = et - 9. Solving for t, we have t = ln(x + 9).
Substituting t = ln(x + 9) into equation (b), we get y = e^(2ln(x + 9)) = e^(ln(x + 9)^2) = (x + 9)^2.
Therefore, the Cartesian equation of the curve is y = (x + 9)^2.