If one diameter of an ellipse bisects the chords parallel to another, then the second one bisects the chords parallel to the first. These types of diameters are called conjugate diameters.
The midpoints of chords parallel to y = mx **** on the line b2x + a2my = 0. Hence, the midpoints of the chords parallel to b2x + a2my = 0 whose slope is
-b2/a2m lie on the line
That is, the midpoints of the parallel chords lie on the line y = mx.
