Two circles C, and C2 both pass through the points A(l ,2) and E(2, 1) and touch the line  4x−2y=9 at B and D, respectively. The possible coordinates of a point C such that the quadrilateral ABCD is a parallelogram , are (a, b). Then the value of ab is _________

The radical axis bisects the common tangent BD.Hence, M is the mid Point of BD.Let C≡(a,b)C(a, b) lies on common chord AE which is y−2=−1(x−1)or x+y=3 Therefore,a + b = 3………………(i)Also Ma+12,b+22 lies on 4x−2y=9 therefore,4a+12−2b+22=9or 2a+2−b−2=9or 2a−b=9……….(ii)Solving (i) and (ii), a = 4 and b = -1. Therefore   ab= -4