(i) An ellipse has eccentricity e=43. The sum of the lengths of its major and minor axes is 25 cm. Find the numerical values of a,b and c.
(ii) Write the standard equation of this ellipse when its centre is at the origin and the major axis is along the x-axis.
(iii) Determine the co-ordinates of its foci and the end-points of its latus rectum.
(iv) Calculate the length of the latus rectum and verify, by direct substitution, that any point P(a,0) on the ellipse satisfies the defining property that the sum of its focal distances equals the length of the major axis.