JEE Exam > JEE Questions > The equation of the parabola with vertex at (...
Start Learning for Free
The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:
- a)y2 = – 2x
- b)x2 = – 8y
- c)y2 = – 8x
- d)x2 = – 4y
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
The equation of the parabola with vertex at (0, 0) and focus at (0, &n...
Given the vertex of the parabola is (0,0) and focus is at (0,-2).
This gives the axis of the parabola is the positive y− axis.
Then the equation of the parabola will be x^2 = 4ay where a = -2.
So the equation of the parabola is x2 = -8y.
This gives the axis of the parabola is the positive y− axis.
Then the equation of the parabola will be x^2 = 4ay where a = -2.
So the equation of the parabola is x2 = -8y.
Community Answer
The equation of the parabola with vertex at (0, 0) and focus at (0, &n...
Understanding the Parabola
A parabola is defined by its focus and directrix. The vertex is the midpoint between these two points. In this case, we have:
- Vertex: (0, 0)
- Focus: (0, -2)
Orientation of the Parabola
Since the focus is located below the vertex, the parabola opens downward. The standard form of a parabola that opens vertically is given by:
- Equation: y² = 4px
Where 'p' is the distance from the vertex to the focus.
Calculating p
The distance from the vertex (0, 0) to the focus (0, -2) is 2 units. Hence, p = -2 (negative because it opens downward).
Forming the Equation
Substituting p into the standard form:
- y² = 4(-2)x
- y² = -8x
Thus, the equation of the parabola becomes:
Final Equation
- y² = -8x
This matches option (b).
Conclusion
The correct equation for the parabola with a vertex at (0, 0) and a focus at (0, -2) is indeed:
- y² = -8x
A parabola is defined by its focus and directrix. The vertex is the midpoint between these two points. In this case, we have:
- Vertex: (0, 0)
- Focus: (0, -2)
Orientation of the Parabola
Since the focus is located below the vertex, the parabola opens downward. The standard form of a parabola that opens vertically is given by:
- Equation: y² = 4px
Where 'p' is the distance from the vertex to the focus.
Calculating p
The distance from the vertex (0, 0) to the focus (0, -2) is 2 units. Hence, p = -2 (negative because it opens downward).
Forming the Equation
Substituting p into the standard form:
- y² = 4(-2)x
- y² = -8x
Thus, the equation of the parabola becomes:
Final Equation
- y² = -8x
This matches option (b).
Conclusion
The correct equation for the parabola with a vertex at (0, 0) and a focus at (0, -2) is indeed:
- y² = -8x
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 equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect answer is option 'B'. Can you explain this answer?
Question Description
The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect 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 The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect 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 The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect answer is option 'B'. Can you explain this answer?.
The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect 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 The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect 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 The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect 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 The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The equation of the parabola with vertex at (0, 0) and focus at (0, – 2) is:a)y2= – 2xb)x2= – 8yc)y2= – 8xd)x2= – 4yCorrect 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
|
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