A hyperbola has its transverse axis along the x–axis, eccentricity e=35, and the distance between its foci is 20 units.
a. (i) Calculate the values of c, a, and b.
b. (ii) Write the standard equation of the hyperbola.
c. (iii) Determine the coordinates of the vertices and the equations of the asymptotes.
d. (iv) Draw a neat sketch of the hyperbola, clearly indicating the centre, vertices, foci, and asymptotes. Use an appropriate scale so that the relative proportions are correct.