Conic Sections: Hyperbolas

Asymptotes of a Hyperbola

Asymptotes of a horizontal and vertical hyperbola

Hyperbolas have asymptotes, much like the rational functions we learned about in previous sections. The blue dashed lines represent the asymptotes of the hyperbola. Remember that the graph of the hyperbola will approach these lines but will never cross them.

If the standard equation of a hyperbola is x squared divided by a squared minus y squared divided by b squared equals 1 then the equation of the asymptotes is y equals plus or minus b divided by a times x .

If the standard equation of a hyperbola is y squared divided by a squared minus x squared divided by b squared equals 1 then the equation of the asymptotes is y equals plus or minus a divided by b times x .