Good morning everybody. I would like to know the proof of the following observation on the ellipse.
A circle is drawn with the right latus rectum as diameter. Another circle is drawn with its center on the major axis such that it is internally tangent to both the circle given above, and the auxiliary circle (the circumcircle of the ellipse). This circle is said to be right associate circle of ellipse. (The left associate circle is defined similarly.) All the circles whose diameters are right focal chords are tangent to the right associate circle, and similarly, all the circles whose diameters are left focal chords are tangent to the left associate circle.
Also, can we see something similar in the other conic sections?