JEE Exam > JEE Questions > If a, b, c are in A.P. then the straight line...
Start Learning for Free
If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates are
- a)(1, -2)
- b)(-1, 2)
- c)(1, 2)
- d)(-1, -2)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If a, b, c are in A.P. then the straight line ax + by + c = 0 will alw...
Given, a, b, c are in A.P.
Let the common difference be d.
So, b = a + d and c = a + 2d
Now consider the equation ax + by + c = 0
Substituting the values of b and c, we get
ax + (a + d)y + (a + 2d) = 0
Simplifying this equation, we get
y = -(a/d)x - (a+2d)/d
This is the equation of a straight line in slope-intercept form.
The slope of this line is -a/d, which is constant for any values of a and d.
So, the line will always pass through a fixed point whose coordinates are independent of the values of a and d.
To find this point, we can substitute any two values of a and d and solve for the point of intersection of the two lines.
Substituting a = 1 and d = 1, we get the equation of the first line as y = -x - 3.
Substituting a = 2 and d = 1, we get the equation of the second line as y = -2x - 4.
Solving these two equations, we get the point of intersection as (1, -2).
Hence, the fixed point through which the given line always passes is (1, -2).
Therefore, the correct answer is option A.
Let the common difference be d.
So, b = a + d and c = a + 2d
Now consider the equation ax + by + c = 0
Substituting the values of b and c, we get
ax + (a + d)y + (a + 2d) = 0
Simplifying this equation, we get
y = -(a/d)x - (a+2d)/d
This is the equation of a straight line in slope-intercept form.
The slope of this line is -a/d, which is constant for any values of a and d.
So, the line will always pass through a fixed point whose coordinates are independent of the values of a and d.
To find this point, we can substitute any two values of a and d and solve for the point of intersection of the two lines.
Substituting a = 1 and d = 1, we get the equation of the first line as y = -x - 3.
Substituting a = 2 and d = 1, we get the equation of the second line as y = -2x - 4.
Solving these two equations, we get the point of intersection as (1, -2).
Hence, the fixed point through which the given line always passes is (1, -2).
Therefore, the correct answer is option A.
Free Test
FREE
| Start Free Test |
Community Answer
If a, b, c are in A.P. then the straight line ax + by + c = 0 will alw...
Given, a, b, c are in A.P.
We know that in an A.P., the common difference (d) is a constant.
Let the common difference be d. Therefore, b = a + d and c = a + 2d.
The equation of the line passing through (x1, y1) and (x2, y2) is given by:
(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)
Let the fixed point be (x, y). Therefore, the equation of the line passing through (a, 1), (b, -2), and (c, 4) is:
(1 - y)/(-2 - y) = (a - x)/(b - x)
(-2 - y)/4-y = (b - x)/(c - x)
On solving the above two equations, we get:
x = (a + 2b + 2c)/5 and y = (-2a - b + 2c)/5
Therefore, the fixed point is (1, -2). Hence, option A is the correct answer.
We know that in an A.P., the common difference (d) is a constant.
Let the common difference be d. Therefore, b = a + d and c = a + 2d.
The equation of the line passing through (x1, y1) and (x2, y2) is given by:
(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)
Let the fixed point be (x, y). Therefore, the equation of the line passing through (a, 1), (b, -2), and (c, 4) is:
(1 - y)/(-2 - y) = (a - x)/(b - x)
(-2 - y)/4-y = (b - x)/(c - x)
On solving the above two equations, we get:
x = (a + 2b + 2c)/5 and y = (-2a - b + 2c)/5
Therefore, the fixed point is (1, -2). Hence, option A is the correct answer.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer?
Question Description
If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer?.
If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer?.
Solutions for If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If a, b, c are in A.P. then the straight line ax + by + c = 0 will always pass through a fixed point whose coordinates area)(1, -2)b)(-1, 2)c)(1, 2)d)(-1, -2)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup