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.