JEE Exam > JEE Questions > A hyperbola passing through origin has 3x &nd...
Start Learning for Free
A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis is
- a)x – y – 5 = 0
- b)x + y + 1 = 0
- c)x + y – 5 = 0
- d)x – y – 1 = 0
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A hyperbola passing through origin has 3x – 4y – 1 = 0 and...
Asymptotes are equally inclined to the axes of hyperbola Find the bisector of the asymptotes which bisects the angle containing the origin.
Most Upvoted Answer
A hyperbola passing through origin has 3x – 4y – 1 = 0 and...
Given Information:
- Equation of one asymptote: 3x - 4y - 1 = 0
- Equation of the other asymptote: 4x - 3y - 6 = 0
Explanation:
Finding the Slope of the Asymptotes:
1. Write the equations of the asymptotes in the form of y = mx + c.
2. Compare the coefficients of x and y to find the slopes of the asymptotes.
- For the first asymptote: slope = 3/4
- For the second asymptote: slope = 4/3
Equation of Transverse Axis:
3. Since the hyperbola passes through the origin, its center is also at the origin.
4. The transverse axis of the hyperbola passes through the center and is parallel to the asymptotes.
5. The equation of the transverse axis in the form of y = mx + c is given by y = x.
6. To find the equation in the form Ax + By + C = 0, we rearrange y = x to get x - y = 0.
7. Therefore, the equation of the transverse axis is x + y = 0, which can be rewritten as x + y - 0 = 0 or x + y = 0.
Conclusion:
The equation of the transverse axis of the hyperbola passing through the origin with asymptotes 3x - 4y - 1 = 0 and 4x - 3y - 6 = 0 is x + y = 0, which is option 'C'.
- Equation of one asymptote: 3x - 4y - 1 = 0
- Equation of the other asymptote: 4x - 3y - 6 = 0
Explanation:
Finding the Slope of the Asymptotes:
1. Write the equations of the asymptotes in the form of y = mx + c.
2. Compare the coefficients of x and y to find the slopes of the asymptotes.
- For the first asymptote: slope = 3/4
- For the second asymptote: slope = 4/3
Equation of Transverse Axis:
3. Since the hyperbola passes through the origin, its center is also at the origin.
4. The transverse axis of the hyperbola passes through the center and is parallel to the asymptotes.
5. The equation of the transverse axis in the form of y = mx + c is given by y = x.
6. To find the equation in the form Ax + By + C = 0, we rearrange y = x to get x - y = 0.
7. Therefore, the equation of the transverse axis is x + y = 0, which can be rewritten as x + y - 0 = 0 or x + y = 0.
Conclusion:
The equation of the transverse axis of the hyperbola passing through the origin with asymptotes 3x - 4y - 1 = 0 and 4x - 3y - 6 = 0 is x + y = 0, which is option 'C'.
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
A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct answer is option 'C'. Can you explain this answer?
Question Description
A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct 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 A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct 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 A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct answer is option 'C'. Can you explain this answer?.
A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct 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 A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct 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 A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct answer is option 'C'. Can you explain this answer?.
Solutions for A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct 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 A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A hyperbola passing through origin has 3x – 4y – 1 = 0 and 4x – 3y – 6 = 0 as its asymptotes. Then the equation of its transverse axis isa)x – y – 5 = 0b)x + y + 1 = 0c)x + y – 5 = 0d)x – y – 1 = 0Correct 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
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup