Transverse axis

Definition

The transverse axis of a hyperbola is the line segment that passes through both foci and its length is equal to the distance between the vertices. It lies along the direction in which the hyperbola opens.

5 Must Know Facts For Your Next Test

1. The transverse axis intersects the center of the hyperbola.
2. Its length is denoted as $2a$, where $a$ is the distance from the center to each vertex.
3. For a horizontal hyperbola, the transverse axis lies along the x-axis; for a vertical hyperbola, it lies along the y-axis.
4. The equation of a hyperbola in standard form $(x^2/a^2 - y^2/b^2 = 1)$ defines its transverse axis.
5. The endpoints of the transverse axis are called vertices.

Review Questions

• How do you determine whether a hyperbola's transverse axis is horizontal or vertical?
• What is the relationship between the length of the transverse axis and parameter $a$?
• Where does the transverse axis intersect on a coordinate plane?

Related terms

Conjugate Axis: The conjugate axis of a hyperbola is perpendicular to the transverse axis and bisects it at its midpoint.

Vertices: Points where each branch of a hyperbola meets its respective end of the transverse axis.

$a$ (Semi-major Axis): $a$ represents half of the length of the transverse axis in a hyperbola.