Mathematics

Mathematics

Problem

Let T be the line passing through the point P(−2, 7) and Q(2, −5). Let F1F_1 be the set of all circles (S1,S2S_1, S_2) such that T is tangent to S1S_1 at P and tangent to S2S_2 at Q and also such that S1S_1 and S2S_2 touch each other at a point say, M. Let E1E_1 be the set representing the locus of M as the pairs (S1,S2S_1, S_2) varies in F1F_1. Let the set of all straight line segment joining a pair of distinct point of E1E_1 and passing through the point R(1, 1) be F2F_2. Let E2E_2 be the set of the mid-point of the line segment in the set F2F_2. Then which of the following statements is true? (A) The point (4, −6) lies in E1E_1 (B) The point (45,75)\left(\frac{4}{5}, \frac{7}{5}\right) does not lie in E1E_1 (C) The point (12,1)\left(\frac{1}{2}, 1\right) lies on E2E_2 (D) The point (0,32)\left(0, \frac{3}{2}\right) does not lie in E2E_2 (A) The point (4, −6) lies in E1E_1 (B) The point (45,75)\left(\frac{4}{5}, \frac{7}{5}\right) does not lie in E1E_1 (C) The point (12,1)\left(\frac{1}{2}, 1\right) lies on E2E_2 (D) The point (0,32)\left(0, \frac{3}{2}\right) does not lie in E2E_2

Browse the problem library