The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is the reciprocal of the center of the given circle. The reciprocal of a circle is therefore a conic section whose focus is the center of reciprocation and whose directrix is the line which corresponds to the center of reciprocation. The conic will be an ellipse, hyperbola, or parabola if the center of reciprocation lies inside, outside, or on the given circle, respectively (Lachlan 1893, p. 181).

# Reciprocal Curve

## See also

Duality Principle, Inverse Curve, Inversion Pole, Polar, Reciprocation## Explore with Wolfram|Alpha

## References

Lachlan, R. "Reciprocation." Ch. 11 in*An Elementary Treatise on Modern Pure Geometry.*London: Macmillian, pp. 174-182, 1893.

## Referenced on Wolfram|Alpha

Reciprocal Curve## Cite this as:

Weisstein, Eric W. "Reciprocal Curve."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/ReciprocalCurve.html