Ellipse S1 has its foci at (±3,0) and a vertex at (5,0). Ellipse S2 has its foci at (±4,0) and is known to have the same eccentricity as S1.
Solve the following.
a. (i) For S1, calculate the lengths of the semi-major axis and semi-minor axis, and determine its eccentricity.
b. (ii) For S2, determine the length of its semi-major axis.
c. (iii) For S2, find the length of its latus rectum and state whether it is longer or shorter than that of S1.