Let A(−4,1) and B(6,−9) be two fixed points in the coordinate plane.
(a) Determine the set of all points P(x,y) that are equidistant from A and B.
(b) Show that the locus obtained in part (a) is a straight line, and write its equation in the form px+qy+r=0.
(c) Verify that the point C(1,−4) lies on this line and hence is equidistant from A and B.