Hyperbolas

Symmetry

Hyperbolas have both reflectional and rotational symmetry. The reflectional symmetry of every hyperbola is a vertical line through the center and a horizontal line through the center. The rotational symmetry of every hyperbola is 180 degrees about the center point.

Example State the symmetry for the hyperbola modeled by the equation:

HyperbolaRevised1

Step 1. State the center.

The center of the hyperbola is: (1, -5)

Step 2. State the reflectional symmetry.

This hyperbola has lines of symmetry at x = 1 and y = -5.

Step 3. State the rotational symmetry.

This hyperbola has 180 degree rotational symmetry about (1, -5).