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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?
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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.
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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'.
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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?
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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?.
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