key term - 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

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.