Question

How many asymptotes does a hyperbola have?

Answer 1

Definition of hyperbola:

A hyperbola is the set of all points such that the difference of the distances between any point on the hyperbola and two fixed points is constant. The two fixed points are called the foci of the hyperbola.

The standard equation for a hyperbola with a horizontal transverse axis is$\frac{{\left(x-h\right)}^2}{a^2}-\frac{{\left(y-h\right)}^2}{b^2}=1$. The center is at$(h,k)$. The distance between the vertices is$2a$. The distance between the foci is$2c$. where$c^2=a^2+b^2$.

Every hyperbola has two asymptotes. A hyperbola with a horizontal transverse axis and center at $(h,k)$has asymptotes with equations $y=k\pm \frac{b}{a}(x-h)$