This .NET class wraps the AcGePointOnCurve2d ObjectARX class. 

It represents a point on a 2D parametric curve. This class encapsulates all of the geometric information of a point on a 2D curve, including its parameter value, 2D coordinates, and derivatives.

Autodesk.AutoCAD.Geometry.Entity2d
    Autodesk.AutoCAD.Geometry.PointEntity2d
        Autodesk.AutoCAD.Geometry.PointOnCurve2d

Public sealed Class PointOnCurve2d
Inherits PointEntity2d

public sealed class PointOnCurve2d : PointEntity2d;

Geometry library documentation in ObjectARX Developer's Guide