1.

Let T be the line passing 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 statment(s) is (are) TRUE ?

Answer»

The point (–2,7) LIES in `E_(1)`
The point `((4)/(5), (7)/(5))` does NOTlie in `E_(2)`
The point `((1)/(2), 1)` lies in `E_(2)`
The point `(0, (3)/(2))` does NOTlie in `E_(1)`

Answer :D


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