Pay attention that in step (d) of the solution path outlined in Hint 4, you need to find the foci of the conic sections. These can be found as the intersections of the axes of the conic sections. Finding an axis becomes easier if you take advantage of the fact that some of the conic sections in the figure are degenerate, in the form of simple straight lines.
Please submit the solution to this problem via e-mail to firstname.lastname@example.org. The next hint for the Problem 5 will be published at 13:00 GMT, 7th May 2023, together with the next updates of the intermediate results.