The definition of the ellipse as a locus with constant sum of distances suggests a practical and surprising way to draw it.
Observation — Physical construction with two nails and a string
If we drive two nails into and , tie a string of length to their ends and slide a pencil that keeps the string taut, the pencil will trace out precisely an ellipse. It is a construction used by gardeners to lay out elliptical flower beds.
The reason is immediate: at every instant the taut string represents the sum , which stays equal to the fixed length of the string. Thus every position of the pencil satisfies exactly the condition of the definition.