Consider $$ x(t) = 2 e^{-t} + 3e^{2t}$$
$$y(t) = 5 e^{-t} + 2 e^{2t}$$
which represents a non rectilinear paths
Horizontal and Verical Asymptotes :
If $t \rightarrow +\infty \ \ or \ \ -\infty$, then $x(t) \ \ and \ \ y(t) \ \ \rightarrow \infty$, So there are no asymptotes parallel to coordinate axis
oblique Asymptotes:
Please tell me how to find the Oblique asymptotes
Best Answer
There are no horizontal asymptotes: this would mean $x\to\infty$ and $y\to$ some finite value. For obligue asymptotes look at the limit when $t\to\pm\infty$ of $y/x$. This is a plot of the curve.