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The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent. If the line I passes through the origin, then its equation is
- a)x – y = 0
- b)x + y + 0
- c)x + 2y = 0
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l ar...
Let concurrent point be (h,k)Then both line will satisfies this point h+2k-3=0 and2h+k-3=0 By solving these two equations we geth=1and k=1 thus , we have two points (0,0) and (1,1) Therefore by two. Point form of lineThe equation of given line would be X-Y-1=0
By using family of lines the equation ofL is (x+2y-3)+∆(2x+y-3)=0 ,the line passes through origin (0,0).We get ∆=-1-x-y=0x=y
Most Upvoted Answer
The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l ar...
To solve this problem, let's first find the point of intersection of the two given lines.
Given lines:
1. x + 2y + 3 = 0 ...(1)
2. 2x + y + 3 = 0 ...(2)
To find the point of intersection, we can solve these two equations simultaneously. Subtract equation (2) from equation (1) to eliminate x:
(x + 2y + 3) - (2x + y + 3) = 0
x + 2y + 3 - 2x - y - 3 = 0
-x + y = 0
So, we have -x + y = 0 ...(3)
This equation represents the line passing through the point of intersection of the given lines (1) and (2).
Now let's consider the line l. Since it is concurrent with the given lines, it must pass through the point of intersection of the given lines.
Let's assume the equation of line l is ax + by = 0.
Since line l passes through the point of intersection (-1, -1) of the given lines, substituting these values in the equation of line l, we get:
a(-1) + b(-1) = 0
-a - b = 0
a + b = 0 ...(4)
Now, let's consider the line I passing through the origin. We know that the equation of a line passing through the origin can be written as y = mx, where m is the slope of the line.
Let's substitute the values of x = 1 and y = m in equation (4):
1 + m = 0
m = -1
So, the slope of line I is -1. Therefore, the equation of line I is y = -x.
Comparing this equation with the options given, we can see that the correct answer is option A: x + y = 0.
Given lines:
1. x + 2y + 3 = 0 ...(1)
2. 2x + y + 3 = 0 ...(2)
To find the point of intersection, we can solve these two equations simultaneously. Subtract equation (2) from equation (1) to eliminate x:
(x + 2y + 3) - (2x + y + 3) = 0
x + 2y + 3 - 2x - y - 3 = 0
-x + y = 0
So, we have -x + y = 0 ...(3)
This equation represents the line passing through the point of intersection of the given lines (1) and (2).
Now let's consider the line l. Since it is concurrent with the given lines, it must pass through the point of intersection of the given lines.
Let's assume the equation of line l is ax + by = 0.
Since line l passes through the point of intersection (-1, -1) of the given lines, substituting these values in the equation of line l, we get:
a(-1) + b(-1) = 0
-a - b = 0
a + b = 0 ...(4)
Now, let's consider the line I passing through the origin. We know that the equation of a line passing through the origin can be written as y = mx, where m is the slope of the line.
Let's substitute the values of x = 1 and y = m in equation (4):
1 + m = 0
m = -1
So, the slope of line I is -1. Therefore, the equation of line I is y = -x.
Comparing this equation with the options given, we can see that the correct answer is option A: x + y = 0.
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The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent. If the line I passes through the origin, then its equation isa)x – y = 0b)x + y + 0c)x + 2y = 0d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent. If the line I passes through the origin, then its equation isa)x – y = 0b)x + y + 0c)x + 2y = 0d)none of theseCorrect answer is option 'A'. 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 The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent. If the line I passes through the origin, then its equation isa)x – y = 0b)x + y + 0c)x + 2y = 0d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent. If the line I passes through the origin, then its equation isa)x – y = 0b)x + y + 0c)x + 2y = 0d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent. If the line I passes through the origin, then its equation isa)x – y = 0b)x + y + 0c)x + 2y = 0d)none of theseCorrect answer is option 'A'. 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 The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent. If the line I passes through the origin, then its equation isa)x – y = 0b)x + y + 0c)x + 2y = 0d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent. If the line I passes through the origin, then its equation isa)x – y = 0b)x + y + 0c)x + 2y = 0d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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