Suppose that the point P from Hint 1 is the centre of the lens O and that the circle introduced in Hint 1 is the circle whose image (the ellipse) is given in the problem statement. Accordingly, M is the image of T and N is the image of A. Since the line MN is the image of AT, if we were able to draw a line u parallel to AT through O, it would intersect with MN at the focal plane (why?). Assuming we are able to draw a line v through O that is parallel to t, according to Hint 1, the line u can be constructed as the bisector between OM and v.
Please submit the solution to this problem via e-mail to physcs.cup@gmail.com.