Locus of Midpoints of Parallel Chords

Locus of Midpoints of Parallel Chords

For chords of the parabola having a fixed slope, their midpoints lie on a line parallel to the axis of the parabola.

For chord slope $$m$$:

$$y=\frac{x}{m}-\frac{a}{m^3}$$

Usage

- Used to determine the locus of the midpoint when a family of parallel chords is considered.