How to Skew (er) a Parametric Curve: Or, Finding Asymptotes of Nonexplicit Curves Christopher DeBoever, Barbara De Roes, Al Cuoco, E. Paul Goldenberg and William McCallum The Mathematics Teacher , pp.

Yeah, you'd use limits to find the asymptote. You can do that by finding the slope of the line tangent to the curve. To do that, take the derivative of the function.