I'm trying to write an algorithm that will create the smallest possible ellipse to encompass any number of points on 2D euclidean space. I've gotten it to the point where I can attain the major axis A by taking the furthest two points in the set and likewise the centerpoint C as the average of those two furthest points. I now want to loop through the remaining points in the set to find the highest minor axis B value, once the two furthest points are found the remaining points are normalized to them (moved/rotated) such that the center point of the ellipse is the new (0,0) and it is going to be an ellipse with horizontal foci, my question is:(adsbygoogle = window.adsbygoogle || []).push({});

Given the centerpoint of a normalized ellipse, it's major diameter A and any point P laying on the circumference of that ellipse, how do I find the focus F, or the minor diameter B?

If this helps explain it, I have C, a and P of this diagram, I want to find b or f:

http://upload.wikimedia.org/wikipedia/commons/6/65/Ellipse_Properties_of_Directrix_and_String_Construction.svg

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question Regarding Ellipses

**Physics Forums | Science Articles, Homework Help, Discussion**