Let T be the line passing through the point P(−2, 7) and Q(2, −5). Let F1 be the set of all circles (S1,S2) such that T is tangent to S1 at P and tangent to S2 at Q and also such that S1 and S2 touch each other at a point say, M. Let E1 be the set representing the locus of M as the pairs (S1,S2) varies in F1. Let the set of all straight line segment joining a pair of distinct point of E1 and passing through the point R(1, 1) be F2. Let E2 be the set of the mid-point of the line segment in the set F2. Then which of the following statements is true?
(A) The point (4, −6) lies in E1
(B) The point (54,57) does not lie in E1
(C) The point (21,1) lies on E2
(D) The point (0,23) does not lie in E2