Light focusses onto a point I from a point \(\mathrm{O}\) after reflecting off a surface that completely surrounds the two points, as shown in cross section below. The shape of the surface is such that all rays leaving \(\mathrm{O}\) (excepting the single ray which returns to \(\mathrm{O}\) ) reflect to I.

(a) What is the shape of the surface?

(b) Pick any one of the paths. Is it a path of minimum time, maximum time, or is it stationary but of neither minimum nor maximum time for all nearby paths?