Question

Describe the shape of a hyperbola. What is an asymptote of a hyperbola?

Short answer

A hyperbola is a pair of identical, mirror-image curves while an asymptote in the context of a hyperbola, there are two lines that the curve approaches, but never intersects or touches.

Step-by-step solution

Describe the shape of a Hyperbola

A hyperbola is a type of conic section defined as the set of all points in a plane such that the difference of the distances from two fixed points (called the foci) is constant. It consists of two separate branches or curves that open either up and down, or right and left. Each branch is a mirror image of the other.

Explain the concept of Asymptotes

Asymptotes are lines that a curve approaches but never touches or crosses. They essentially provide a boundary for the curve's behavior.

Describe the Asymptotes of a Hyperbola

In the case of a hyperbola, there are two asymptotes, which cross at the center of the hyperbola. The hyperbola's branches approach these asymptotes but never cross them. The equations of the asymptotes can be found using the standard equation of the hyperbola.