Let A(2,3) and B(−4,7) be two fixed points. A point P(x,y) moves in the plane such that the area of △APB is 12 square units.
a. (i) Derive the equation satisfied by the coordinates (x,y) of the point P.
b. (ii) Identify the geometrical nature of this locus.
c. (iii) Calculate the perpendicular distance between the two lines obtained in part (i).