The following VBA example creates two intersecting ellipses and combines them into a single curve. At the intersections of the ellipses (now subpaths), small circles are created.
Sub YPosition()
Dim s1 As Shape, sr As New ShapeRange
Dim s As Shape
Dim cps As CrossPoints
Dim cp As CrossPoint
sr.Add ActiveLayer.CreateEllipse2(4, 4, 3)
sr.Add ActiveLayer.CreateEllipse2(5, 3, 2)
Set s = sr.Combine
Set cps = s.Curve.Subpaths(1).GetIntersections(s.Curve.Subpaths(2))
For Each cp In cps
ActiveLayer.CreateEllipse2 cp.PositionX, cp.PositionY, 0.1
Next cp
End Sub