Consider the three hyperbolas listed below, all centred at the origin:
H₁: 9x2−16y2=1
H₂: 16x2−16y2=1
H₃: 25y2−9x2=1
(i) For each hyperbola, calculate its eccentricity, showing all steps.
(ii) Arrange the three hyperbolas in ascending order of eccentricity.
(iii) Identify which hyperbola has branches that open the widest and give a brief reason based on your results in part (i).