What are the asymptotes of a hyperbola?

[Manni]

I’m studying conic sections and want to understand the concept of asymptotes related to a hyperbola. Can someone explain what the asymptotes are and how to find their equations?

 

[Lucky]

Asymptotes of a hyperbola are straight lines that the hyperbola approaches but never touches. For a hyperbola centered at the origin, the equations are y=±baxy = \pm \frac{b}{a}xy=±abx (for horizontal) or y=±abxy = \pm \frac{a}{b}xy=±bax (for vertical). They help in sketching the hyperbola and understanding its behavior at infinity.

 

[Grace]

The asymptotes of a hyperbola are straight lines that the curve approaches but never meets. They pass through the center of the hyperbola and define its direction and shape.