JEE Exam > JEE Questions > A parabola has the origin as its focus and th...
Start Learning for Free
A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]
- a)(0, 2)
- b)(1, 0)
- c)(0, 1)
- d)(2, 0)
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A parabola has the origin as its focus and the line x = 2 as the direc...
Vertex of a parabola is the mid point of focus and the point
where directrix meets the axis of the parabola.
Here focus is O(0, 0) and directxix meets the axis at B(2, 0)
∴ Vertex of the parabola is (1, 0)
Here focus is O(0, 0) and directxix meets the axis at B(2, 0)
∴ Vertex of the parabola is (1, 0)
Most Upvoted Answer
A parabola has the origin as its focus and the line x = 2 as the direc...
Solution:
The standard equation of a parabola with focus (a, 0) and directrix x = -a is given by:
(x - a)^2 + y^2 = 4a(x + a)
Here, the focus is at the origin (0, 0) and the directrix is x = 2. Thus, we have a = 1.
Substituting a = 1, we get:
(x - 1)^2 + y^2 = 4(x + 1)
Expanding and simplifying, we get:
x^2 - 2x + y^2 = 0
Completing the square, we get:
(x - 1)^2 + y^2 = 1
This is the standard equation of a circle with center at (1, 0) and radius 1. The vertex of the parabola is the point on the axis of symmetry closest to the focus, which is the center of the circle. Therefore, the vertex is (1, 0).
Hence, the correct option is (b) (1, 0).
The standard equation of a parabola with focus (a, 0) and directrix x = -a is given by:
(x - a)^2 + y^2 = 4a(x + a)
Here, the focus is at the origin (0, 0) and the directrix is x = 2. Thus, we have a = 1.
Substituting a = 1, we get:
(x - 1)^2 + y^2 = 4(x + 1)
Expanding and simplifying, we get:
x^2 - 2x + y^2 = 0
Completing the square, we get:
(x - 1)^2 + y^2 = 1
This is the standard equation of a circle with center at (1, 0) and radius 1. The vertex of the parabola is the point on the axis of symmetry closest to the focus, which is the center of the circle. Therefore, the vertex is (1, 0).
Hence, the correct option is (b) (1, 0).
Free Test
FREE
| Start Free Test |
Community Answer
A parabola has the origin as its focus and the line x = 2 as the direc...
Focus of parabola is (
a,0)
Here focus is (0,0)
Therefore a=0
Distance between focus and directrix is 2 times distance between focus and vertex
Let the point be (x,0) (since the point is on x axis)
2(x-a)=(2-a)
2x=2
x =1
The required point is (1,0)
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
|
|
Top Courses for JEEView all
A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer?
Question Description
A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. 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 A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer?.
A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. 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 A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer?.
Solutions for A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. 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 A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at [2008]a)(0, 2)b)(1, 0)c)(0, 1)d)(2, 0)Correct answer is option 'B'. 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup