Let T be the line passing through the points  $P(-2,7)andQ(2,-5).$ 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 $S_1\&S_2$ touch each other at 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?