Two ellipses P and Q have the same length of latus rectum L=6 cm but different semi-major axes aP=5 cm and aQ=8 cm.
Answer the following.
(i) Show that the eccentricity e of any ellipse can be expressed as e2=1−2aL, where a is its semi-major axis and L is the length of its latus rectum.
(ii) Using the relation in part (i), find the eccentricities eP and eQ.
(iii) If the latus rectum length is kept constant while the semi-major axis is increased further, explain qualitatively how the eccentricity will change and what this implies about the shape of the ellipse.