A hyperbola approaches its asymptotes arbitrarily closely as the distance from its center increases, but it never intersects them; however, a degenerate hyperbola consists only of its asymptotes. Source: Internet
Conic section analysis of the hyperbolic appearance of circles Figure 10: The hyperbola as a circle on the ground seen in perspective while gazing down slightly, showing the circle's (non-parallel) tangents as asymptotes. Source: Internet
Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph. Source: Internet
A similar argument shows that the lower left branch of the curve also has the same two lines as asymptotes. Source: Internet
Asymptotes for rational functions A rational function has at most one horizontal asymptote or oblique (slant) asymptote, and possibly many vertical asymptotes. Source: Internet
Functions may lack horizontal asymptotes on either or both sides, or may have one horizontal asymptote that is the same in both directions. Source: Internet