An asymptote of an unbounded curve is a straight line whose distance from the curve tends to zero along a specified end. For a graph, a sloping asymptote satisfies as tends to the relevant infinity. Factorization of the leading quadratic part locates the two asymptotes of a nondegenerate hyperbola.

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Asymptote can refer to two primary concepts: one in mathematics and the other as a programming language for technical graphics. 1. **Mathematical Concept**: In mathematics, an asymptote is a line that a curve approaches as it heads towards infinity. Asymptotes can be horizontal, vertical, or oblique (slant). They represent the behavior of a function as the input or output becomes very large or very small.