Defence Exam > Defence Questions > P : x2 – y2 + 2y – 1 = 0L : x + y...
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P : x2 – y2 + 2y – 1 = 0
L : x + y = 3
L : x + y = 3
Q.
If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' is
- a)x2 – y2 – 4x + 2y + 3 = 0
- b)x2 – y2 – 2x + 4y – 3 = 0
- c)x2 – y2 + 2x – 4y – 3 = 0
- d)x2 – y2 + 4x – 2y + 3 = 0
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represent...
To find the equation of the line L', we first need to find the point of intersection of the lines P.
Step 1: Find the point of intersection of P
Given equations:
P: x^2 - y^2 = 2y - 1 ...(1)
L: x + y = 3 ...(2)
To find the point of intersection, we can solve equations (1) and (2) simultaneously.
Substituting y = 3 - x in equation (1), we get:
x^2 - (3 - x)^2 = 2(3 - x) - 1
Simplifying the above equation, we get:
x^2 - 9 + 6x - x^2 = 6 - 2x - 1
Combining like terms, we get:
7x - 10 = -2x + 5
Bringing all the terms to one side, we get:
9x = 15
Dividing by 9, we get:
x = 15/9 = 5/3
Substituting the value of x in equation (2), we get:
5/3 + y = 3
y = 3 - 5/3
y = 4/3
Therefore, the point of intersection of P is (5/3, 4/3).
Step 2: Find the equation of L'
Since L' is perpendicular to L and passes through the point of intersection, its slope will be the negative reciprocal of the slope of L.
The slope of L can be found by rearranging equation (2) in slope-intercept form:
y = -x + 3
Comparing with the slope-intercept form y = mx + c, we can see that the slope of L is -1.
The slope of L' will be the negative reciprocal of -1, which is 1.
Using the point-slope form, we can write the equation of L' as:
y - 4/3 = 1(x - 5/3)
y - 4/3 = x - 5/3
y = x - 5/3 + 4/3
y = x - 1/3
Therefore, the equation of L' is x - y + 1/3 = 0.
Step 3: Write the pair of lines representing L and L'
The pair of lines representing L and L' can be written as:
L: x + y = 3
L': x - y + 1/3 = 0
Step 4: Simplify the equations
Multiplying equation L' by 3 to get rid of the fraction, we get:
3x - 3y + 1 = 0
Therefore, the simplified equations representing L and L' are:
L: x + y = 3
L': 3x - 3y + 1 = 0
Comparing the simplified equations with the given options, we can see that option B:
x^2 - y^2 - 2x + 4y - 3 = 0
matches the equations L and L'.
Therefore, the
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P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represent...
Given Information:
- Equations of the lines P and L are provided.
- Line L is perpendicular to line L and passes through the point of intersection of lines P.
Steps to find the equation of lines representing L and L:
1. Find the point of intersection of lines P:
- Solve the equations x^2 + y^2 + 2y - 1 = 0 and x + y = 3 to find the point of intersection.
2. Find the slope of line L:
- The slope of line L is the negative reciprocal of the slope of line L.
3. Use the point-slope form to find the equation of line L:
- Use the point of intersection and the slope of L to write the equation of L.
4. Find the equation of line L:
- The equation of line L will be perpendicular to L and pass through the point of intersection.
5. Write the final equation of the pair of lines representing L and L:
- Combine the equations of L and L to represent the pair of lines.
Therefore, the equation representing the pair of lines L and L is x^2 - y^2 - 2x + 4y - 3 = 0, which corresponds to option B.
- Equations of the lines P and L are provided.
- Line L is perpendicular to line L and passes through the point of intersection of lines P.
Steps to find the equation of lines representing L and L:
1. Find the point of intersection of lines P:
- Solve the equations x^2 + y^2 + 2y - 1 = 0 and x + y = 3 to find the point of intersection.
2. Find the slope of line L:
- The slope of line L is the negative reciprocal of the slope of line L.
3. Use the point-slope form to find the equation of line L:
- Use the point of intersection and the slope of L to write the equation of L.
4. Find the equation of line L:
- The equation of line L will be perpendicular to L and pass through the point of intersection.
5. Write the final equation of the pair of lines representing L and L:
- Combine the equations of L and L to represent the pair of lines.
Therefore, the equation representing the pair of lines L and L is x^2 - y^2 - 2x + 4y - 3 = 0, which corresponds to option B.
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P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' isa)x2 – y2 – 4x + 2y + 3 = 0b)x2 – y2 – 2x + 4y – 3 = 0c)x2 – y2 + 2x – 4y – 3 = 0d)x2 – y2 + 4x – 2y + 3 = 0Correct answer is option 'B'. Can you explain this answer?
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P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' isa)x2 – y2 – 4x + 2y + 3 = 0b)x2 – y2 – 2x + 4y – 3 = 0c)x2 – y2 + 2x – 4y – 3 = 0d)x2 – y2 + 4x – 2y + 3 = 0Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' isa)x2 – y2 – 4x + 2y + 3 = 0b)x2 – y2 – 2x + 4y – 3 = 0c)x2 – y2 + 2x – 4y – 3 = 0d)x2 – y2 + 4x – 2y + 3 = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' isa)x2 – y2 – 4x + 2y + 3 = 0b)x2 – y2 – 2x + 4y – 3 = 0c)x2 – y2 + 2x – 4y – 3 = 0d)x2 – y2 + 4x – 2y + 3 = 0Correct answer is option 'B'. Can you explain this answer?.
P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' isa)x2 – y2 – 4x + 2y + 3 = 0b)x2 – y2 – 2x + 4y – 3 = 0c)x2 – y2 + 2x – 4y – 3 = 0d)x2 – y2 + 4x – 2y + 3 = 0Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' isa)x2 – y2 – 4x + 2y + 3 = 0b)x2 – y2 – 2x + 4y – 3 = 0c)x2 – y2 + 2x – 4y – 3 = 0d)x2 – y2 + 4x – 2y + 3 = 0Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' isa)x2 – y2 – 4x + 2y + 3 = 0b)x2 – y2 – 2x + 4y – 3 = 0c)x2 – y2 + 2x – 4y – 3 = 0d)x2 – y2 + 4x – 2y + 3 = 0Correct answer is option 'B'. Can you explain this answer?.
Solutions for P : x2 – y2 + 2y – 1 = 0L : x + y = 3Q.If L' represents the line perpendicular to L passing through the point of intersection of the pair of lines P, then equation of the pair of lines representing L and L' isa)x2 – y2 – 4x + 2y + 3 = 0b)x2 – y2 – 2x + 4y – 3 = 0c)x2 – y2 + 2x – 4y – 3 = 0d)x2 – y2 + 4x – 2y + 3 = 0Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
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