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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?
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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).
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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)
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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?
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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?.
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