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A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lies between them. Find the equation of the line if its distances from these lines are in the ratio 3:5 ?
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A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lie...
Given Information:
- Two lines: 3x-y-3 = 0 and 3x-y-5 = 0
- The unknown line is parallel to the given lines and lies between them
- The distances from the unknown line to the given lines are in the ratio 3:5
Approach:
1. Find the equations of the perpendicular bisectors of the given lines.
2. The unknown line will be parallel to the perpendicular bisector and equidistant from the given lines.
3. Use the ratio of distances to find the equation of the unknown line.
Perpendicular Bisectors of the Given Lines:
1. The given lines can be rewritten in the form y = 3x - 3 and y = 3x - 5
2. The slopes of the given lines are 3 and 3 respectively
3. The slopes of the perpendicular bisectors will be -1/3 and -1/3 respectively
4. The midpoints of the given lines are (0, -3/2) and (0, -5/2)
5. The equations of the perpendicular bisectors are y = -1/3x - 3/2 and y = -1/3x - 5/2
Equation of the Unknown Line:
1. The unknown line will have the same slope as the perpendicular bisectors, which is -1/3
2. Let the equation of the unknown line be y = -1/3x + c
3. The unknown line is equidistant from the given lines, so the distance from the unknown line to the first given line is 3k and to the second given line is 5k
4. Use the distance formula to find the value of c and hence the equation of the unknown line.
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A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lies between them. Find the equation of the line if its distances from these lines are in the ratio 3:5 ?
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A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lies between them. Find the equation of the line if its distances from these lines are in the ratio 3:5 ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lies between them. Find the equation of the line if its distances from these lines are in the ratio 3:5 ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lies between them. Find the equation of the line if its distances from these lines are in the ratio 3:5 ?.
A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lies between them. Find the equation of the line if its distances from these lines are in the ratio 3:5 ? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lies between them. Find the equation of the line if its distances from these lines are in the ratio 3:5 ? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A straight line is parallel to the lines 3x-y-3 =0 & 3x-y 5 =0 and lies between them. Find the equation of the line if its distances from these lines are in the ratio 3:5 ?.
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