The fixed points A(−2,3) and B(6,7) are the ends of one side of a variable triangle △ABP. The point P(x,y) moves so that the area of the triangle is always 15 square units.
(i) Derive the equation of the locus of P.
(ii) Show that the locus consists of two parallel straight lines.
(iii) Determine the perpendicular distance between these two lines.