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

 

[blue_raver22]

I understand that math can be daunting for those who haven't studied it in a while. Let me help break down the concept of latus rectum for you in a simple way.

The latus rectum is a geometric term used to describe a specific chord in an ellipse. It is defined as the line segment perpendicular to the major axis that passes through the focus (one of the two fixed points in an ellipse) and has both endpoints on the ellipse. In simpler terms, it is the longest chord that can be drawn in an ellipse.

In your case, the length of the latus rectum can be found using the formula l = 2b^2/a, where a is the length of the major axis and b is the length of the minor axis. Plugging in the values you provided (a=165, b=80), we can calculate that the length of the latus rectum in your ellipse is approximately 160.

I hope this explanation helps you understand the concept of latus rectum and how to calculate it in your specific case. If you need further assistance, please don't hesitate to reach out. Best of luck with your animation project!