Axes of symmetry

Definition

Axes of symmetry are lines that divide a figure into two mirror-image halves. In hyperbolas, these axes typically refer to the transverse and conjugate axes.

5 Must Know Facts For Your Next Test

1. The transverse axis is the line segment that passes through the vertices of the hyperbola.
2. The conjugate axis is perpendicular to the transverse axis and intersects it at the center of the hyperbola.
3. The lengths of the transverse and conjugate axes are $2a$ and $2b$ respectively, where $a$ and $b$ are constants derived from the hyperbola's equation.
4. In standard position, a hyperbola centered at $(h,k)$ has its transverse axis along either the x-axis or y-axis depending on its orientation.
5. The asymptotes of a hyperbola intersect at right angles to both axes of symmetry.

Review Questions

• What is the relationship between the transverse axis and vertices of a hyperbola?
• How do you determine whether a hyperbola's transverse axis is horizontal or vertical?
• What role does the conjugate axis play in defining a hyperbola?

Related terms

Transverse Axis:

The line segment passing through both foci and vertices of a hyperbola.

Conjugate Axis:

The line segment perpendicular to the transverse axis that intersects it at the center.

Asymptote:

A line that a curve approaches as it heads towards infinity, intersecting at angles with axes of symmetry in hyperbolas.