TITLE: Ellipse like on sphere
QUESTION [11 upvotes]: Find the locus of all points on a sphere such that the sum of  geodesic distances from two fixed points $F_1$ and $F_2$ on it is a constant, less than its diameter. ( When radius of sphere goes to infinity, it would look like an ellipse).
Following is image after Equn  ($1$) in achille hui note

REPLY [2 votes]: In response to queries by ebin zheng:
Achille hui has taken unit radius for the sphere. However if we denote it by $a$ we have 
$$ \frac{x^2}{D^2} + \frac{y^2}{D^2-A^2} = \frac{a^2}{1+D^2}\tag{**1}$$
and you wish to recover planar ellipse as $ a \rightarrow \infty. $