# Equation for the length of a chord parallel to either the minor or major axis in an ellipse

I am looking for a way to compute the length of any chord parallel to the minor (or major) axis of an ellipse. In all cases I know the lengths of both axes, and the distance between the chord and axis (the right bisector). I can calculate this easily with circles using the length of the right bisector, but am not sure how to adapt my approach to ellipses.

As some background, I am using this to create elliptical discs of random points in a computer graphics visualization. Thank you!

• How are the chords you want to find the lenghts of specified? – hmakholm left over Monica Jul 22 '14 at 15:21
• @HenningMakholm Makholm - I'm not sure I understand your question. I know the lengths of the minor and major axes, and want to know how to compute the length of any chord parallel to one of those axes. I also know the distance of the chord from the axis. Does this clarify? – gromiczek Jul 22 '14 at 15:23

If the major and minor axes of the ellipse are $2a$ and $2b$, then the length of the chord parallel to the major axis at a distance of $x$ is $$2a\sqrt{1-(x/b)^2}$$ For a chord parallel to the minor axis, interchange $a$ and $b$.