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If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0 then
(1)All lines are parallel
(2) All lines are inconsistence
(3) All lines are concurrent at ()
(4) All lines are concurrent at (3,2)?
(1)All lines are parallel
(2) All lines are inconsistence
(3) All lines are concurrent at ()
(4) All lines are concurrent at (3,2)?
Most Upvoted Answer
If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0...
Given Information:
px + qy + r = 0 represents a family of straight lines
3p + 24 + 4r = 0
Solution:
Equation of the Family of Lines:
The equation px + qy + r = 0 represents a family of straight lines passing through a fixed point. Here, p, q, and r are constants.
Equation of the given Line:
3p + 24 + 4r = 0 represents a specific line in the family of lines.
Analysis:
Case 1: All lines are parallel
If the lines are parallel, then the coefficients of x and y in the family of lines' equation will be proportional. However, in this case, the coefficients do not indicate parallel lines.
Case 2: All lines are inconsistent
If the lines are inconsistent, there will be no solution to the system of equations represented by the family of lines. But, in this case, the lines are consistent.
Case 3: All lines are concurrent at a point
For all lines to meet at a point, the constants in the family of lines' equation should satisfy the given line's equation. By substituting 3p + 24 + 4r = 0 into px + qy + r = 0, we can determine if all lines pass through a common point.
Verification:
Substitute 3p + 24 + 4r = 0 into px + qy + r = 0:
p(3) + q(2) + r = 0
3p + 2q + r = 0
Now, compare this equation with 3p + 24 + 4r = 0:
2q = 24
q = 12
Since q is fixed at 12, the lines are concurrent at a point. However, the specific point of concurrency is not given. Therefore, the correct answer is:
(3) All lines are concurrent at a point.
px + qy + r = 0 represents a family of straight lines
3p + 24 + 4r = 0
Solution:
Equation of the Family of Lines:
The equation px + qy + r = 0 represents a family of straight lines passing through a fixed point. Here, p, q, and r are constants.
Equation of the given Line:
3p + 24 + 4r = 0 represents a specific line in the family of lines.
Analysis:
Case 1: All lines are parallel
If the lines are parallel, then the coefficients of x and y in the family of lines' equation will be proportional. However, in this case, the coefficients do not indicate parallel lines.
Case 2: All lines are inconsistent
If the lines are inconsistent, there will be no solution to the system of equations represented by the family of lines. But, in this case, the lines are consistent.
Case 3: All lines are concurrent at a point
For all lines to meet at a point, the constants in the family of lines' equation should satisfy the given line's equation. By substituting 3p + 24 + 4r = 0 into px + qy + r = 0, we can determine if all lines pass through a common point.
Verification:
Substitute 3p + 24 + 4r = 0 into px + qy + r = 0:
p(3) + q(2) + r = 0
3p + 2q + r = 0
Now, compare this equation with 3p + 24 + 4r = 0:
2q = 24
q = 12
Since q is fixed at 12, the lines are concurrent at a point. However, the specific point of concurrency is not given. Therefore, the correct answer is:
(3) All lines are concurrent at a point.
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If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0 then (1)All lines are parallel (2) All lines are inconsistence (3) All lines are concurrent at () (4) All lines are concurrent at (3,2)?
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If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0 then (1)All lines are parallel (2) All lines are inconsistence (3) All lines are concurrent at () (4) All lines are concurrent at (3,2)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0 then (1)All lines are parallel (2) All lines are inconsistence (3) All lines are concurrent at () (4) All lines are concurrent at (3,2)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0 then (1)All lines are parallel (2) All lines are inconsistence (3) All lines are concurrent at () (4) All lines are concurrent at (3,2)?.
If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0 then (1)All lines are parallel (2) All lines are inconsistence (3) All lines are concurrent at () (4) All lines are concurrent at (3,2)? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0 then (1)All lines are parallel (2) All lines are inconsistence (3) All lines are concurrent at () (4) All lines are concurrent at (3,2)? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If px+qy+r=0 represent a family of straight lines such that 3p+24+4r=0 then (1)All lines are parallel (2) All lines are inconsistence (3) All lines are concurrent at () (4) All lines are concurrent at (3,2)?.
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