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# Horizontal Asymptotes

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In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity . Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors. [1] In projective geometry and related contexts, an asymptote of a curve is a line which is tangent to the curve at a point at infinity . [2] [3]