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) $TRUE$?

• A
  The point $(-2, 7)$ lies in $E_1$
• B
  The point $(\frac{4}{5}, \frac{7}{5})$ does $NOT$ lie in $E_2$
• C
  The point $(\frac{1}{2}, 1)$ lies in $E_2$
• D
  The point $(0, \frac{3}{2})$ does $NOT$ lie in $E_1$