Add the multifocal ellipsoid

Test-problems.md

@@ -23,7 +23,7 @@ for some positive $r$, $s$. Show that $A$, $B$, $C$, $D$, $E$, $F$ must be the v
 
 ## Exploring configuration spaces
 
-### Equiangular equilateral hexagons
+### The configuration space of equiangular, equilateral hexagons
 
 #### Source
 
@@ -42,6 +42,23 @@ O’Hara has described the configuration space of hexagons in 3-space which are
 
 According to Dan Piker, the configuration space of right-angled equilateral heptagons also has at least one one-dimensional component.
 
+### Generalized conic: multifocal ellipsoid
+
+#### Source
+
+Two-dimensional version
+
+- **Author:** James Clerk Maxwell
+- **Published:** ["Paper on the Description of Oval Curves"](https://www.google.com/books/edition/The_Scientific_Letters_and_Papers_of_Jam/zfM8AAAAIAAJ?hl=en&gbpv=1&pg=PA35) (February 1846), in *The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862*
+
+#### Statement
+
+Fix two or more “pin” points in 2-space or 3-space. Constrain a movable “pencil” point by running a fixed-length string through all the points in some sequence. Find the locus of possible positions of the pencil.
+
+#### Notes
+
+To avoid topological issues, it would be simplest to model the length of the string as a whole-number linear combination of the distances from the points to the pencil. To get an ellipse, use two pins and fix the sum of the distances (with unit coefficients).
+
 ## Hierarchical constraints
 
 These problems impose various kinds of *soft constraints* on top of the *hard constraints* that an assembly must satisfy to qualify as a solution. Here are some possible kinds of soft constraints.