# How to find out asymptotes for any algebraic curve?

1. Jan 13, 2014

### s0ft

There are a lot of contents regarding finding vertical, horizontal and oblique asymptotes for the so called 'rational' functions online. All of these curves are given in the form y=f(x)=(g(x))/(h(x)).
But as far as my search results go, there are none regarding general algebraic curves/polynomials.
I'd like to know, for example, how do you find all the asymptotes for the curve:
$y^3 - x^2y + 2y^2 +4y + x = 0$
i.e. for a curve of the form:
$f(x,y) = 0$ where an explicit definition for $y$ has not been provided or would be inconvenient?

2. Jan 13, 2014

### epenguin

Well that one you find them by looking what happens when x and y become very large and you can neglect certain terms as being numerically negligible compared to certain others.

Last edited: Jan 13, 2014