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Hyperbola question

2018 · Shift 2 · Q20

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PYQ Library
JEE Advanced
Mathematics
Hyperbola
2018 · Shift 2 · Q20

Hyperbola question

2018 · Shift 2 · Q20

JEE AdvancedMathematicsHyperbolaMultiple correct+4 / −1

Let T be the line passing through the points P(

-

2, 7) and Q(2,

-

5). Let F1 be the set of al 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 $\left( {{4 \over 5},{7 \over 5}} \right)$ does not lie in E2
C
The point $\left( {{1 \over 2},1} \right)$ lies in E2
D
The point $\left( {0,{3 \over 2}} \right)$ does not lie in E1

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