Defence Exam > Defence Questions > A circle always passes through the fixed poin...
Start Learning for Free
A circle always passes through the fixed points (a, 0) and (–a, 0).
Q.
The radius of the circle x2 + y2 + x + c = 0 passing through the origin is
- a)1/4
- b)1/2
- c)1
- d)2
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A circle always passes through the fixed points (a, 0) and (–a, ...
Given equation of circle is x^2 + y^2 + x c = 0
To find the radius of the circle passing through origin, we need to find the distance between the origin and the center of the circle.
Let (h, k) be the center of the circle.
Since the circle passes through (a, 0), we can use the distance formula to get:
√((h-a)^2 + k^2) = |h-a|
Since the circle also passes through (-a, 0), we can use the distance formula again to get:
√((h+a)^2 + k^2) = |h+a|
Squaring both equations, we get:
(h-a)^2 + k^2 = (h+a)^2 + k^2
Simplifying, we get:
h = a/2
Substituting this value of h in either equation, we get:
k = √(3a^2/4)
The distance between the origin and the center of the circle is:
r = √(h^2 + k^2) = √(a^2/4 + 3a^2/4) = √(a^2) / 2 = a/2
Therefore, the radius of the circle passing through the origin is a/2.
The correct answer is option B) 1/2.
To find the radius of the circle passing through origin, we need to find the distance between the origin and the center of the circle.
Let (h, k) be the center of the circle.
Since the circle passes through (a, 0), we can use the distance formula to get:
√((h-a)^2 + k^2) = |h-a|
Since the circle also passes through (-a, 0), we can use the distance formula again to get:
√((h+a)^2 + k^2) = |h+a|
Squaring both equations, we get:
(h-a)^2 + k^2 = (h+a)^2 + k^2
Simplifying, we get:
h = a/2
Substituting this value of h in either equation, we get:
k = √(3a^2/4)
The distance between the origin and the center of the circle is:
r = √(h^2 + k^2) = √(a^2/4 + 3a^2/4) = √(a^2) / 2 = a/2
Therefore, the radius of the circle passing through the origin is a/2.
The correct answer is option B) 1/2.
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer?
Question Description
A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer?.
A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer?.
Solutions for A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A circle always passes through the fixed points (a, 0) and (–a, 0).Q.The radius of the circle x2 + y2 + x + c = 0 passing through the origin isa)1/4b)1/2c)1d)2Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup