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 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 midpoints of the line segments in the set $F_2.$ Then, which of the following statement(s) is (are) TRUE?