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!
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 $b$.