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Let T be the line passing through the ...

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 lines 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? The point `(-2, 7)` lies in `E_1` (b) The point `(4/5,7/5)` does NOT lie in `E_2` (c) The point `(1/2, 1)` lies in `E_2` (d) The point `(0,3/2)` does NOT lie in `E_1`

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