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)).(adsbygoogle = window.adsbygoogle || []).push({});

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:

[itex]y^3 - x^2y + 2y^2 +4y + x = 0[/itex]

i.e. for a curve of the form:

[itex]f(x,y) = 0[/itex] where an explicit definition for [itex]y[/itex] has not been provided or would be inconvenient?

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# How to find out asymptotes for any algebraic curve?

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