Given a drawing of an ellipse is there any geometric construction we can do to find it's foci?
Solution 1:
Take two parallel lines $l_1,l_2$ cutting the ellipse in $A_1,B_1,A_2,B_2$. Let $C_i$ be the midpoint of $A_i B_i$: the center of the ellipse lies on the $C_1 C_2$ line. Once the center $O$ of the ellipse is found, take a circle with center $O$ cutting the ellipse in the vertices of a rectangle: the symmetry axis of the rectangle are the axis of the ellipse too, hence the vertices of the ellipse are found. Given the center and the vertices, to find the foci of an ellipse is an easy task:
