Transverse axis

Definition

The transverse axis of a hyperbola is the line segment that passes through both foci and whose endpoints are the vertices. It lies along the major axis of the hyperbola.

5 Must Know Facts For Your Next Test

1. The length of the transverse axis is equal to $2a$, where $a$ is the distance from the center to a vertex.
2. The transverse axis runs horizontally for hyperbolas centered at $(h, k)$ with equation $\dfrac{(x-h)^2}{a^2} - \dfrac{(y-k)^2}{b^2} = 1$.
3. For hyperbolas with vertical orientation, the equation is $\dfrac{(y-k)^2}{a^2} - \dfrac{(x-h)^2}{b^2} = 1$, and the transverse axis runs vertically.
4. The midpoint of the transverse axis is the center of the hyperbola.
5. Vertices lie on the transverse axis, while co-vertices lie on the conjugate axis.

Review Questions

• What is the length of the transverse axis for a hyperbola with vertices at $(3,0)$ and $(-3,0)$?
• In which direction does the transverse axis run for a hyperbola with equation $\dfrac{(y+4)^2}{16} - \dfrac{(x-3)^2}{9} = 1$?
• How do you find the center of a hyperbola if you know its transverse axis?

Related terms

Vertices: Points on a hyperbola located at $(h+a,k)$ and $(h-a,k)$ or $(h,k+a)$ and $(h,k-a)$ depending on orientation.

Conjugate Axis: The line segment perpendicular to the transverse axis that passes through the center of a hyperbola.

Foci: Fixed points located inside each branch of a hyperbola used to define its shape; they are located along the transverse axis.