Equal Sums of Distances to Two Pairs of Points
This activity belongs to the GeoGebra book GeoGebra Principia.
If we input XA + XB = XC, the resulting locus corresponds to the intersection of a family of ellipses
XA + XB = k
and a family of circles
XC = k
as the parameter k varies.
In the case of four points, XA + XB = XC + XD corresponds to the intersection of two families of ellipses.
- Note: Calculating the minimum and maximum values of k that ensure intersection is not straightforward. An approach can be seen in [6].
Author of the construction of GeoGebra: Rafael Losada.