Question

Let T be the line passing through the points P(-2, 7) and Q(2, -5). Let F₁ be the set of all pairs of circles


(S₁, S₂) such that T is tangent to S₁ at P and tangent to S₂ at Q, and also such that S₁ and S₂ touch each other


at a point, say, M. Let E₁ be the set representing the locus of M as the pair (S₁, S₂) varies in F₁. Let the set


of all straight line segments joining a pair of distinct points of E₁ and passing through the point R(1, 1) be


F₂. Let E₂ 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 (B) The point(4/5 , 7/5) does NOT lie in E₂


(C) The point (1/2,1) lies in E₂ (D) The point (0, 3/2) does NOT lie in E₁

Answer 1

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