Let $T$  be the line passing through the points $P (-2, 7)$ and $Q (2,-5).$ Let $F_1$  be the set of all pairs of circles $(S_1.S_2)$ such that $T$  is tangent to $S_1$  at P and tangent to $S_2$  at Q, and also such that  $S_1$and $S_2$  touch each other at a point, say, M. Let  $E_1$  be the set representing the locus of M as the pair $(S_1,S_2)$ varies in $F_1$ . Let the set of all straight line segments Joining a pair of distinct points of $E_1$  and passing through the point $R (1, 1)$ be $F_2$ . Let  $E_2$  be the set of the mid-points of the line segments in the set $F_2$ . Then, which of the following statement(s) is (are) TRUE?