Hello,

the equation is given by

$\sum_{j=1}^2 s_j = 2a$

where

$s_j = |P_i - F_j|$

is the distance between the i-th point and the j-th focal point. Parameter a denotes the major semi-axis.

This model is also valid for the spatial case, cf. Lösler, M. and Nitschke, M., 2010. Bestimmung der Parameter einer Regressionsellipse in allgemeiner Raumlage. Allgemeine Vermessungs-Nachrichten, Vol. 117(3), pp. 113-117

and can be used to parametrize an elliptical cylinder, cf. Lösler, M. 2020. Modellierung und Bestimmung eines elliptischen Zylinders. Allgemeine Vermessungs-Nachrichten, Vol. 127(2), pp. 87-93

Kind regards
Micha