Quant Exam > Quant Questions > A circle has its centre at the origin and a p...
Start Learning for Free
A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.
- a)out side
- b)on
- c)none of these
- d)in side
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A circle has its centre at the origin and a point P(5, 0) lies on it. ...
Most Upvoted Answer
A circle has its centre at the origin and a point P(5, 0) lies on it. ...
Explanation:
To determine the position of point Q(8, 6) with respect to the circle, we need to compare the distance between the center of the circle (origin) and point Q with the radius of the circle.
Step 1: Calculate the distance between the center of the circle (origin) and point Q using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((8 - 0)^2 + (6 - 0)^2)
= √(8^2 + 6^2)
= √(64 + 36)
= √100
= 10
Step 2: Compare the distance between the center and point Q with the radius of the circle. Since the center is at the origin, the radius of the circle is the distance between the origin and point P(5, 0).
Radius = √((5 - 0)^2 + (0 - 0)^2)
= √(5^2 + 0^2)
= √25
= 5
Step 3: Compare the distance with the radius:
- If the distance is greater than the radius, point Q lies outside the circle.
- If the distance is equal to the radius, point Q lies on the circle.
- If the distance is less than the radius, point Q lies inside the circle.
In this case, the distance between the center and point Q is 10, which is greater than the radius of the circle (5). Therefore, point Q lies outside the circle.
Conclusion: The point Q(8, 6) lies outside the circle. Therefore, the correct answer is option A) outside.
To determine the position of point Q(8, 6) with respect to the circle, we need to compare the distance between the center of the circle (origin) and point Q with the radius of the circle.
Step 1: Calculate the distance between the center of the circle (origin) and point Q using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((8 - 0)^2 + (6 - 0)^2)
= √(8^2 + 6^2)
= √(64 + 36)
= √100
= 10
Step 2: Compare the distance between the center and point Q with the radius of the circle. Since the center is at the origin, the radius of the circle is the distance between the origin and point P(5, 0).
Radius = √((5 - 0)^2 + (0 - 0)^2)
= √(5^2 + 0^2)
= √25
= 5
Step 3: Compare the distance with the radius:
- If the distance is greater than the radius, point Q lies outside the circle.
- If the distance is equal to the radius, point Q lies on the circle.
- If the distance is less than the radius, point Q lies inside the circle.
In this case, the distance between the center and point Q is 10, which is greater than the radius of the circle (5). Therefore, point Q lies outside the circle.
Conclusion: The point Q(8, 6) lies outside the circle. Therefore, the correct answer is option A) outside.
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer?
Question Description
A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer?.
A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A circle has its centre at the origin and a point P(5, 0) lies on it. Then the point Q(8, 6) lies ________ the circle.a)out sideb)onc)none of thesed)in sideCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant 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