Question

X= e^t -9 , y= e^2t Find the cartesian equation

Answer 1

$\bf \begin{cases} x=e^t-9\\\\ y=e^{2t} \end{cases}\\\\ -----------------------------\\\\ x=e^t-9\implies x+9=e^t\implies ln(x+9)=ln(e^t) \\\\\\ ln(x+9)=\underline{t}\\\\ -----------------------------\\\\ y=e^{2t}\iff y=e^{2\underline{ln(x+9)}}$