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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 F2 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)
- c)
- d)
Correct answer is option 'B,D'. Can you explain this answer?
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Verified Answer
Let T be the line passing through the points P(−2,7) and Q (2,&m...
The following figure shows the required condition in the question.
The values of different angles are given as.
The expression for ∠QC2M and ∠PC1M is as follows.
The equation of locus for the variable point M is given as.
(x + 2)(x − 2)+ (y − 7)(y + 5) =0
From the equation of locus for the variable point M, it is clear that the equation does not contain point P and Q. The point P will be included when the radius of circle S1 is zero and consequently Q will be included when the radius of circle S2 is zero. If radius of both the circles is zero then, the circle becomes a straight line, which is not possible.
Therefore, the set E1 does not contain P and Q.
The locus of mid point chords passing through (1,1) is given as,
It is clear from the above equation, that line passing through P (−2, 7 ) and R (1,1) is as follows.
y + 2x − 3=0
The centre of locus of M is given as,
C3 ( 0,1)
The foot of the locus of M on the equation (A) is
which
is also the mid point of chord PR of circle x2 +y2−2y−39 = 0 .
Since, point P is not a part of the locus M then PQ is not the chord of locus of M.
Hence, option (B) and (D) are correct.
The values of different angles are given as.
The expression for ∠QC2M and ∠PC1M is as follows.
The equation of locus for the variable point M is given as.
(x + 2)(x − 2)+ (y − 7)(y + 5) =0
From the equation of locus for the variable point M, it is clear that the equation does not contain point P and Q. The point P will be included when the radius of circle S1 is zero and consequently Q will be included when the radius of circle S2 is zero. If radius of both the circles is zero then, the circle becomes a straight line, which is not possible.
Therefore, the set E1 does not contain P and Q.
The locus of mid point chords passing through (1,1) is given as,
It is clear from the above equation, that line passing through P (−2, 7 ) and R (1,1) is as follows.
y + 2x − 3=0
The centre of locus of M is given as,
C3 ( 0,1)
The foot of the locus of M on the equation (A) is
which is also the mid point of chord PR of circle x2 +y2−2y−39 = 0 .
Since, point P is not a part of the locus M then PQ is not the chord of locus of M.
Hence, option (B) and (D) are correct.
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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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer?
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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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer?.
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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer?.
Solutions for 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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer?, a detailed solution for 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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer? has been provided alongside types of 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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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 theset 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 F2 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 E1b)c)d)Correct answer is option 'B,D'. Can you explain this answer? tests, examples and also practice JEE tests.
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