JEE Exam > JEE Questions > The centres of a set of circles, each of radi...
Start Learning for Free
The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set is
- a)4 ≤ x2+y2 ≤ 64
- b)x2+y2 ≤ 25 [2002]
- c)x2+y2 ≥ 25
- d)3 ≤ x2+y2 ≤ 9
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The centres of a set of circles, each of radius 3, lie on the circle x...
For any point P (x, y) in the given circle,
we should have
OA ≤ OP ≤ OB ⇒ (5-3) 
⇒ 4 ≤ x2 +y2 ≤ 64
Most Upvoted Answer
The centres of a set of circles, each of radius 3, lie on the circle x...
The equation of the circle is x^2 + y^2 = 25, which means that the center of the circle lies on this circle. Let's call the center of the circle (a, b).
Since the radius of each circle is 3, the coordinates of any point on the circle can be represented as (a + 3cosθ, b + 3sinθ), where θ is the angle between the positive x-axis and the line connecting the center of the circle and the point on the circle.
Substituting these coordinates into the equation of the circle, we get:
(a + 3cosθ)^2 + (b + 3sinθ)^2 = 25
Expanding and simplifying, we get:
a^2 + 2a(3cosθ) + 9cos^2(θ) + b^2 + 2b(3sinθ) + 9sin^2(θ) = 25
Rearranging and using the trigonometric identity sin^2(θ) + cos^2(θ) = 1, we get:
a^2 + b^2 + 9 + 6a(cosθ) + 6b(sinθ) = 25
Simplifying further, we get:
a^2 + b^2 + 6a(cosθ) + 6b(sinθ) = 16
This equation represents the locus of any point in the set of circles.
Since the radius of each circle is 3, the coordinates of any point on the circle can be represented as (a + 3cosθ, b + 3sinθ), where θ is the angle between the positive x-axis and the line connecting the center of the circle and the point on the circle.
Substituting these coordinates into the equation of the circle, we get:
(a + 3cosθ)^2 + (b + 3sinθ)^2 = 25
Expanding and simplifying, we get:
a^2 + 2a(3cosθ) + 9cos^2(θ) + b^2 + 2b(3sinθ) + 9sin^2(θ) = 25
Rearranging and using the trigonometric identity sin^2(θ) + cos^2(θ) = 1, we get:
a^2 + b^2 + 9 + 6a(cosθ) + 6b(sinθ) = 25
Simplifying further, we get:
a^2 + b^2 + 6a(cosθ) + 6b(sinθ) = 16
This equation represents the locus of any point in the set of circles.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer?.
The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer?.
Solutions for The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The centres of a set of circles, each of radius 3, lie on the circle x2+y2=25. The locus of any point in the set isa)4 ≤ x2+y2 ≤ 64b)x2+y2 ≤ 25 [2002]c)x2+y2 ≥ 25d)3 ≤ x2+y2 ≤ 9Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup