A set of all points P(x,y) in the plane satisfies the condition that the difference of its distances from the two fixed points F1(−7,0) and F2(7,0) is 8 units.
a. (i) Find the equation of the locus.
b. (ii) Determine the coordinates of the vertices and the value of b.
c. (iii) Calculate the eccentricity.
d. (iv) Obtain the equations of the asymptotes of the curve.