Mathematics Exam > Mathematics Questions > In conics, the _____ is revolving to form two...
Start Learning for Free
In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.
- a)Ellipse
- b)Circle
- c)Generator
- d)Parabola
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In conics, the _____ is revolving to form two anti-parallel cones join...
In conics, the generator is revolving to form two anti-parallel cones joined at the apex. The plane is then made to cut these cones and we get different conic sections. If we cut at right angles with respect to the axis of the cone we get a circle.
Most Upvoted Answer
In conics, the _____ is revolving to form two anti-parallel cones join...
Understanding Conics and the Generator
In the study of conic sections, the concept of a **generator** plays a crucial role, particularly when discussing the formation of different conic shapes.
What is a Generator?
- A generator is a line that, when moved, creates a three-dimensional surface.
- In the context of conics, the generator can be rotated around a fixed axis to form various conic shapes.
Formation of Cones
- When a straight line (the generator) revolves around a fixed line (the axis), it generates a cone.
- If the generator is tilted at an angle, it can create two anti-parallel cones that meet at an apex.
Why ‘C’ is Correct: The Parabola
- The parabola is formed when the plane intersects one of the cones parallel to the slant height of the cone.
- The cones formed by the revolving generator are fundamental in understanding the properties of parabolas.
Comparison with Other Options
- **Ellipse**: Formed when a plane intersects both cones at an angle.
- **Circle**: A special case of an ellipse where the plane is perpendicular to the axis.
- **Parabola (Correct Answer)**: The unique formation resulting from the intersection parallel to the cone's generating line.
Conclusion
- Thus, the **generator** is essential in the study of conics, particularly in forming the parabola through its unique intersection with the cone. This understanding solidifies why the correct answer to the question is option ‘C’.
In the study of conic sections, the concept of a **generator** plays a crucial role, particularly when discussing the formation of different conic shapes.
What is a Generator?
- A generator is a line that, when moved, creates a three-dimensional surface.
- In the context of conics, the generator can be rotated around a fixed axis to form various conic shapes.
Formation of Cones
- When a straight line (the generator) revolves around a fixed line (the axis), it generates a cone.
- If the generator is tilted at an angle, it can create two anti-parallel cones that meet at an apex.
Why ‘C’ is Correct: The Parabola
- The parabola is formed when the plane intersects one of the cones parallel to the slant height of the cone.
- The cones formed by the revolving generator are fundamental in understanding the properties of parabolas.
Comparison with Other Options
- **Ellipse**: Formed when a plane intersects both cones at an angle.
- **Circle**: A special case of an ellipse where the plane is perpendicular to the axis.
- **Parabola (Correct Answer)**: The unique formation resulting from the intersection parallel to the cone's generating line.
Conclusion
- Thus, the **generator** is essential in the study of conics, particularly in forming the parabola through its unique intersection with the cone. This understanding solidifies why the correct answer to the question is option ‘C’.
|
Explore Courses for Mathematics exam
|
|
Similar Mathematics Doubts
Question Description
In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer?.
In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer?.
Solutions for In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.a)Ellipseb)Circlec)Generatord)ParabolaCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mathematics tests.
|
|
Explore Courses for Mathematics exam
|
|
Signup to solve all Doubts
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!
within 7 days!
Takes less than 10 seconds to signup