Axes of symmetry

Definition

Axes of symmetry in hyperbolas are the lines that pass through the center and divide the hyperbola into two symmetrical parts. They include the transverse axis, which passes through the vertices, and the conjugate axis, which is perpendicular to it.

5 Must Know Facts For Your Next Test

1. The transverse axis is aligned with the real axis of a hyperbola.
2. The conjugate axis is perpendicular to the transverse axis and passes through the center of the hyperbola.
3. The length of the transverse axis is $2a$, where $a$ is the distance from the center to a vertex.
4. The length of the conjugate axis is $2b$, where $b$ is related to $a$ and $c$ by $c^2 = a^2 + b^2$.
5. Axes of symmetry help in determining key features such as vertices, foci, and asymptotes.

Review Questions

• What are the axes of symmetry for a hyperbola?
• How do you determine the lengths of the transverse and conjugate axes?
• Why are axes of symmetry important in analyzing a hyperbola?

Related terms

Transverse Axis: A line segment that passes through both vertices of a hyperbola.

Conjugate Axis: A line segment that passes through the center of a hyperbola and is perpendicular to its transverse axis.

Vertices: Points where each branch of a hyperbola intersects its transverse axis.