You are on the right path with graphicspath.
You create 2 graphics paths and add the ellipses defined by a rectangle.
Create 2 regions based on the path constructors
calling r.Intersect will transform r into the region you are looking for
conversely, calling r2.Intersect will transform r2 into the region you are looking for
Dim path1 As New Drawing2D.GraphicsPath()
path1.AddEllipse(New Rectangle(0, 0, 10, 20))
Dim path2 As New Drawing2D.GraphicsPath()
path2.AddEllipse(New Rectangle(0, 0, 10, 20))
Dim r As New Region(path1)
Dim r2 As New Region(path2)
r.Intersect(path2)