Let T be the line passing through the points P(-2, 7) and Q(2,-5). Let F, be...

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Let T be the line passing through the points P(-2, 7) and Q(2,-5). Let F, be the set of all pairs of circles (S₁, S₂) such that T is tangent to S, at P and tangent to S, at Q, and also such that S, and S, touch each other at a point, say, M. Let E, be the set representing the locus of Mas the pair (S₁, S₂) varies in F₁. Let the set of all straight line segments joining a pair of distinct points of E, and passing through the point R(1, 1) be F₂. Let E, be the set of the mid-points of the line segments in the set F₂. Then, which of the following statement(s) is (are) TRUE? (A) The point (-2, 7) lies in E₁ 4 7 (B) The point 5 5 does NOT lie in E2 (C) The point (1) ,1 lies in E₂ E2 3 (D) The point 0, 2 does NOT lie in E₁ Let T be the line passing through the points P(-2, 7) and Q(2,-5). Let F, be the set of all pairs of circles (S₁, S₂) such that T is tangent to S, at P and tangent to S, at Q, and also such that S, and S, touch each other at a point, say, M. Let E, be the set representing the locus of Mas the pair (S₁, S₂) varies in F₁. Let the set of all straight line segments joining a pair of distinct points of E, and passing through the point R(1, 1) be F₂. Let E, be the set of the mid-points of the line segments in the set F₂. Then, which of the following statement(s) is (are) TRUE? (A) The point (-2, 7) lies in E₁ 4 7 (B) The point 5 5 does NOT lie in E2 (C) The point (1) ,1 lies in E₂ E2 3 (D) The point 0, 2 does NOT lie in E₁

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