Points A and B have coordinates \(( - 2,1 )\) and \(( 3,4 )\) respectively. Find the equation of the perpendicular bisector of AB and show that it may be written as \(5 x + 3 y = 10\).
Points C and D have coordinates \(( - 5,4 )\) and \(( 3,6 )\) respectively. The line through C and D has equation \(4 y = x + 21\). The point E is the intersection of CD and the perpendicular bisector of AB . Find the coordinates of point E .
Find the equation of the circle with centre E which passes through A and B . Show also that CD is a diameter of this circle.