In fact, consider a point A on the ellipse and the corresponding point F on the auxiliary circle, having the same ordinate x with A. The tangents of the ellipse at A and the auxiliary circle at F respectively intersect at the same point A* of the major axis. This is discussed in Ellipse.html . This implies easily that the polars of points A* on the x-axis are the same with respect to both the ellipse and its auxiliary circle. This has an interesting consequence. Consider two points X, Y of the ellipse defining a chord, which passes through the point A* of the x-axis. Consider also the corresponding points X*, Y* of the auxiliary circle, having the same abscissas with these points. Then the chord of the circle through X*, Y* passes also trhough A*.

For the relation of the polars for points A* other than the points of x-axis see the file CommonPolar2.html .

Auxiliary.html

CommonPolar2.html

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