James Tanton [url=http://twitter.com/jamestanton/status/608240289136836608]asked[/url]: Reflect an ellipse across each tangent line to it. What curve(s) do the images of its two foci trace?[br][br]The [color=#ff0000][b]ellipse[/b][/color] shown below can be modified by dragging the three [color=#ff0000][b]red points[/b][/color].

Perhaps surprisingly, the curves generated by the reflected foci are circles. As [url=https://twitter.com/CmonMattTHINK/status/608290373312638977]pointed out by Matt Enlow[/url], this is because, in the visual above, the segment lengths [b][color=#0000ff]a[/color][/b] and [b][color=#007700]b[/color][/b] must always sum to the same constant.