Midpoint theorem (conics)

In geometry, the midpoint theorem describes a property of parallel chords in a conic. It states that the midpoints of parallel chords in a conic are located on a common line.

The common line or line segment for the midpoints is called the diameter. For a circle, ellipse or hyperbola the diameter goes through its center. For a parabola the diameter is always perpendicular to its directrix and for a pair of intersecting lines (from a degenerate conic) the diameter goes through the point of intersection.

Gallery ($$e$$ = eccentricity):