An isosceles triangle has two congruent legs of length 1. The Steiner circumellipse of the triangle is then drawn, and the foci of the ellipse are marked.

Question 1: Is it possible for the foci to lie upon the pair of congruent legs of the triangle? If so, how long is the triangle's base?

Question 2: Is it possible for one focus to lie upon the base of the triangle? If so, how long is the triangle's base?