# The foci of an ellipse, reflected across its tangents (2)

James Tanton asked: Reflect an ellipse across each tangent line to it. What curve(s) do the images of its two foci trace?
The

**ellipse**shown below can be modified by dragging the three**red points**.Perhaps surprisingly, the curves generated by the reflected foci are circles. As pointed out by Matt Enlow, this is because, in the visual above, the segment lengths

**a**and**b**must always sum to the same constant.Download our apps here: