Find the locus of the middle points of a system of parallel chords of an ellipse?
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Locus of the mid points of parallel chords of an ellipse is called diameter of the ellipse. Two diameters are said to be conjugate when each bisects all chords parallel to the other. Two diameters y=m1x and y=m2x of the ellipse a2x2+b2y2=1,(∗) are conjugate if m1m2=a2−b2.
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