Two diameters of an ellipse which bisects chords parallel to each other are called conjugated diameters . Therefore the diameters y = mx and y = m1x of the ellipse x^2/a^2 +y^2/b^2 = 1 are conjugate if m*m1 = -b^2/a^2.

In an ellipse, the major axes bisects all chords parallel to the minor axes and vice-versa, therefore major axes and minor axes of an ellipse are conjugate diameters but they do not satisfy the condition m*m1 = -b^2/a^2 and are the only perpendicular conjugate diameters.