The Concentric Circle construction of the ellipse

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The points \(F_1\) and \(F_2\) are the focal points of the ellipse, which determine the major axis (the line \(F_1 F_2\)) and the minor axis (the perpendicular bisector of \(F_1 F_2\)). The two blue circles have centre \(O\) (the midpoint of \(F_1 F_2\)).
Given any ray from the centre, let \(X\) and \(Y\) be the two points where it intersects the inner and outer circle respectively. Now draw a line parallel to the major axis which passes through \(X\), and draw a line parallel to the minor axis which passes through \(Y\) (these two lines are drawn in red in the diagram). The concentric circle construction says that these two lines will intersect at a point \(A\) on the ellipse.
You can click and drag the points \(O\), \(P\) and \(Q\) to move the centre and the major/minor axes. You can pause the animation and click and drag the point \(Y\) to change the orientation of the ray from the centre.