Find the foci of an ellispe
Find the foci of a given ellipse using a compass and a straight edge.
Trivial, but instructive.
1. Find the center of the ellipse:
Construct 2 parallel chords of the ellipse. The straight line connecting their midpoints passes through the center. Repeat with another pair of chords, and we find the center. This works because the ellipse is a parallel projection of a circle.
2. Find the axes of the ellipse.
Construct a circle concentric with the ellipse that intersects it at 4 points. Connect the midpoints of the sides of the rectangle. This works because the axes of the ellipse are its axes of symmetry.
3. Find the foci.
Construct a circle with the center at the end of the minor axis with the radius equal to the major semi-axis. It intersects the major axis at the foci.