Consider the curve given by 9x2+16y2=144.
a. (i) Reduce this equation to the standard form of an ellipse and obtain the values of a and b.
b. (ii) Calculate the eccentricity of the ellipse and the length of its latus rectum.
c. (iii) Find the coordinates of the centre, the vertices, the co-vertices and the foci.
d. (iv) Sketch the ellipse on graph paper, clearly marking and labelling all the points found in part (iii).