Latus rectum for the non-mathematician

[bhnh]

I'm hoping someone can help me with this question. I'm an animator; the last math course I took was 40 years ago.

I have an elliptical shape wherein the major and minor axes intersect off-center, so I've got an egg shape (major axis=165, minor axis =80, intersection at 100,40). I have a line perpendicular to the major axis which can be positioned at any point along the major axis. What I need is a basic algorithm to figure the length of the resulting chord (latus rectum?).

I wouldn't want to admit to being desperate, but I am, kind of. Any help would be immensely appreciated.

Thanks!

 

[Unrest]

I suppose your shape is two ellipses joined at the minor axis. So you can write an equation for each one, with the origin at the intersection of the axes:

Left side:
x²/65² + y²/40² = 1

Right side:
x²/100² + y²/40² = 1

The length is just 2*y. So rearrange for y:
If the line is on the left side:
length = 2 * sqrt( 40²(1-x²/65²) )
Where x is the distance from the intersection of the axes.

 

[bhnh]

Out of sight. Thanks!

 

[Borek]

Note - this doesn't have to be two ellipses, in which case Unrest's idea will be inaccurate.

There is a lot of different egg-shaped functions, length of the chord will depend on which one is used: http://www.mathematische-basteleien.de/eggcurves.htm