JEE Exam > JEE Questions > The point diametrically opposite to the point...
Start Learning for Free
The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]
- a)(3, – 4)
- b)(–3, 4)
- c)(–3, –4)
- d)(3, 4)
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The point diametrically opposite to the point P(1, 0) on the circle x2...
The given circle is x2 + y2 + 2x + 4y –3 = 0
Centre (–1, –2)
Let Q (α, β) be the point diametrically opposite to the point P(1, 0),
⇒ α = –3, β = – 4, So, Q is (–3, –4)
Most Upvoted Answer
The point diametrically opposite to the point P(1, 0) on the circle x2...
To find the point diametrically opposite to the point P(1, 0) on the circle x^2 + y^2 + 2x + 4y = 0, we first need to rewrite the equation of the circle in the standard form:
(x + 1)^2 - 1 + (y + 2)^2 - 4 = 0
(x + 1)^2 + (y + 2)^2 = 5
This equation represents a circle with center (-1, -2) and radius √5.
Since the point diametrically opposite to P(1, 0) lies on the same line passing through the center of the circle, we can find this point by reflecting P across the center of the circle.
The midpoint of the line segment connecting P(1, 0) and the center of the circle (-1, -2) is the center point of the circle. The midpoint can be calculated as follows:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
= ((1 + (-1))/2, (0 + (-2))/2)
= (0, -1)
Therefore, the center of the circle is (0, -1).
To find the point diametrically opposite to P(1, 0), we reflect P across the center of the circle:
Reflected point = (2 * x_center - x_P, 2 * y_center - y_P)
= (2 * 0 - 1, 2 * (-1) - 0)
= (-1, -2)
Thus, the point diametrically opposite to P(1, 0) on the circle x^2 + y^2 + 2x + 4y = 0 is (-1, -2).
(x + 1)^2 - 1 + (y + 2)^2 - 4 = 0
(x + 1)^2 + (y + 2)^2 = 5
This equation represents a circle with center (-1, -2) and radius √5.
Since the point diametrically opposite to P(1, 0) lies on the same line passing through the center of the circle, we can find this point by reflecting P across the center of the circle.
The midpoint of the line segment connecting P(1, 0) and the center of the circle (-1, -2) is the center point of the circle. The midpoint can be calculated as follows:
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
= ((1 + (-1))/2, (0 + (-2))/2)
= (0, -1)
Therefore, the center of the circle is (0, -1).
To find the point diametrically opposite to P(1, 0), we reflect P across the center of the circle:
Reflected point = (2 * x_center - x_P, 2 * y_center - y_P)
= (2 * 0 - 1, 2 * (-1) - 0)
= (-1, -2)
Thus, the point diametrically opposite to P(1, 0) on the circle x^2 + y^2 + 2x + 4y = 0 is (-1, -2).
Free Test
FREE
| Start Free Test |
Community Answer
The point diametrically opposite to the point P(1, 0) on the circle x2...
Hii
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer?
Question Description
The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. 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 The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer?.
The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. 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 The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer?.
Solutions for The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. 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 point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The point diametrically opposite to the point P(1, 0) on the circle x2 + y2 + 2x + 4y – 3 = 0 is [2008]a)(3, – 4)b)(–3, 4)c)(–3, –4)d)(3, 4)Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
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