## Hyperbola Inverse Curve

For a Hyperbola with with Inversion Center at the center, the Inverse Curve

 (1) (2)

is a Lemniscate.

For an Inversion Center at the Vertex, the Inverse Curve

 (3) (4)

is a Right Strophoid.

For an Inversion Center at the Focus, the Inverse Curve

 (5) (6)

is a Limaçon, where is the Eccentricity.

For a Hyperbola with and Inversion Center at the Vertex, the Inverse Curve

 (7) (8)

is a Maclaurin Trisectrix.

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, p. 203, 1972.