Lessons taught; Lessons learnt

Fix two points in the plane, and consider all the quadratics which go through those two points.

Find the locus of the stationary points of these quadratics.

The following Geogebra worksheet might help. If you select “Show stationary point” and move the blue point, it will trace out the locus.

Geogebra applet (enable Java to see it).

(Source: quadratic_stationary_points.ggb.)

Thinking about this question kept me from going to bed until far too late on Thursday. My answer, and other thoughts, will appear tomorrow.

Related Posts (automatically generated)

1. A journey through a mathematical puzzle
2. Visualisation: Yet more rotating squares!
3. Visualisation: More rotating squares