Design a hyperbola centred at the origin whose vertices are at (±4,0) and whose eccentricity is 23.
(i) Find the values of a, b and c.
(ii) Write the standard equation of the hyperbola.
(iii) Determine the coordinates of its foci and equations of its directrices.
(iv) Verify that any vertex of the hyperbola is equidistant from the corresponding focus and the corresponding directrix, thereby confirming the eccentricity value.