Hyperbola

Let T be the line passing through the points P(−2,7) and Q(2,−5) .Let F1 be the set of all pairs of circles (S1,S2) such that T is tangents 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 pair (S1,S2) varies in F1. Let the set of all straight line segments joining a pair of distinct points of E1 and passing through the point R(1, 1) be F2.Let F2 be the set of the mid-points of the line segments in the set F2.Then, which of the following statements(s) is (are) TRUE?