Here is a sample function that you can use to determine if a test point is on a curve:
Public Function IsPointOnCurve(ByVal curve As Curve, ByVal testPoint As Point3d, ByVal tolerance As Double) As Boolean
If (curve IsNot Nothing) Then
Dim t As Double
If (curve.ClosestPoint(testPoint, t)) Then
Dim curvePoint = curve.PointAt(t)
If (testPoint.DistanceTo(curvePoint) <= tolerance) Then
Return True
End If
End If
End If
Return False
End Function