Let A(−3,1) and B(4,7) be fixed points. A moving point P(x,y) satisfies the condition that the numerical value of the area of △ABP equals the perpendicular distance of P from the line AB.
(a) Obtain the Cartesian equation representing the locus of P.
(b) Identify, with justification, the type of conic represented by this equation.
(c) Find the coordinates of the points on the locus that lie on the x-axis.