The dual curve of a plane projective algebraic curve 
is the closure in the dual projective
plane of the set of lines tangent to 
at its nonsingular points. Thus a point of the dual curve
represents a tangent line of the original curve. Singularities of 
and its dual are related by Plücker's
equations.
Dual Curve
See also
Algebraic Curve, Projective Plane, Plücker's Equations, Tangent LineExplore with Wolfram|Alpha
References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, pp. 99-118, 1959.Cite this as:
Weisstein, Eric W. "Dual Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DualCurve.html