6
$\begingroup$

Given a circle, it's easy to contruct its center.

The question is: given an ellipse, draw the foci.

I don't know whether it's possible to do this using only straightedge and compass.

  • 0
    I'm assuming you are given the major and minor axes of the ellipse. Hint: what is the distance from a foci of the ellipse to the "top" of the ellipse?2012-12-21
  • 0
    No, you're only given the ellipse's line, the same way as in the case of the circle.2012-12-21
  • 0
    What do you mean by that? Do you mean you're given the locus of points on the ellipse?2012-12-21
  • 0
    Yes, only that.2012-12-21
  • 0
    Oh yes, of course; sorry for being dense...2012-12-21
  • 0
    Sorry if my answer below is obvious. I can see how this is different from a circle. Given a circle, you could construct any triangle you wanted inside of it, and then locate the circumcenter of the triangle (=center of the circle) with a ruler and compass. I can see that doing something similar for an ellipse does not seem possible.2012-12-21
  • 0
    I wonder if there's something clever to be done with an inscribed trapezoid, or something like that...2012-12-21
  • 0
    @rschwieb , see my solution below.2013-05-11

2 Answers 2