Let A(2,−3) and B(10,5) be fixed points in the plane.
a. (i) Prove that the set of all points P for which PA=PB is the perpendicular bisector of AB, and find its Cartesian equation.
b. (ii) If P is the point on this locus whose x-coordinate is 4, determine the coordinates of P.
c. (iii) Through P draw a line whose slope is 23. A point Q lies on this line such that PQ=6 units. Calculate the coordinates of all possible positions of Q, showing every step of your working.