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If 3a + 2b + 6c = 0, the family of straight lines ax + by + c = 0 passes through a fixed point whose coordinates are given by
- a)(1/2 , 1/3)
- b)(2, 3)
- c)(3, 2)
- d)(1/3 , 1/2)
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If 3a + 2b + 6c = 0, the family of straight lines ax + by + c = 0 pas...
Then, 2x − 1 = 0, 3y − 1 = 0; x = 1/2, y = 1/3
Hence, fixed points is (1/2 ,1/3)
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If 3a + 2b + 6c = 0, the family of straight lines ax + by + c = 0 pas...
To solve this problem, let's first rewrite the given equation in the form of a linear equation:
3a + 2b + 6c = 0
Dividing the entire equation by 6, we get:
a/2 + b/3 + c = 0
This equation represents a family of straight lines in the form of ax + by + c = 0.
To find the fixed point through which all these lines pass, we need to find the values of a, b, and c that satisfy the equation.
Let's choose an arbitrary value for a, say a = 1. Substituting this value in the equation, we get:
1/2 + b/3 + c = 0
Now, let's choose another arbitrary value for b, say b = 1. Substituting this value in the equation, we get:
1/2 + 1/3 + c = 0
Simplifying the equation further:
3/6 + 2/6 + c = 0
5/6 + c = 0
c = -5/6
So, when a = 1 and b = 1, the value of c is -5/6. Therefore, the fixed point through which all the lines in the family pass is (1/2, 1/3, -5/6).
Now, let's check the options given:
a) (1/2, 1/3) - This matches the fixed point we found, so option A is correct.
b) (2, 3) - This does not match the fixed point we found.
c) (3, 2) - This does not match the fixed point we found.
d) (1/3, 1/2) - This does not match the fixed point we found.
Therefore, the correct answer is option A, (1/2, 1/3).
3a + 2b + 6c = 0
Dividing the entire equation by 6, we get:
a/2 + b/3 + c = 0
This equation represents a family of straight lines in the form of ax + by + c = 0.
To find the fixed point through which all these lines pass, we need to find the values of a, b, and c that satisfy the equation.
Let's choose an arbitrary value for a, say a = 1. Substituting this value in the equation, we get:
1/2 + b/3 + c = 0
Now, let's choose another arbitrary value for b, say b = 1. Substituting this value in the equation, we get:
1/2 + 1/3 + c = 0
Simplifying the equation further:
3/6 + 2/6 + c = 0
5/6 + c = 0
c = -5/6
So, when a = 1 and b = 1, the value of c is -5/6. Therefore, the fixed point through which all the lines in the family pass is (1/2, 1/3, -5/6).
Now, let's check the options given:
a) (1/2, 1/3) - This matches the fixed point we found, so option A is correct.
b) (2, 3) - This does not match the fixed point we found.
c) (3, 2) - This does not match the fixed point we found.
d) (1/3, 1/2) - This does not match the fixed point we found.
Therefore, the correct answer is option A, (1/2, 1/3).
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If 3a + 2b + 6c = 0, the family of straight lines ax + by + c = 0 passes through a fixed point whose coordinates are given bya)(1/2 , 1/3)b)(2, 3)c)(3, 2)d)(1/3 , 1/2)Correct answer is option 'A'. Can you explain this answer?
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If 3a + 2b + 6c = 0, the family of straight lines ax + by + c = 0 passes through a fixed point whose coordinates are given bya)(1/2 , 1/3)b)(2, 3)c)(3, 2)d)(1/3 , 1/2)Correct 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 If 3a + 2b + 6c = 0, the family of straight lines ax + by + c = 0 passes through a fixed point whose coordinates are given bya)(1/2 , 1/3)b)(2, 3)c)(3, 2)d)(1/3 , 1/2)Correct 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 If 3a + 2b + 6c = 0, the family of straight lines ax + by + c = 0 passes through a fixed point whose coordinates are given bya)(1/2 , 1/3)b)(2, 3)c)(3, 2)d)(1/3 , 1/2)Correct answer is option 'A'. Can you explain this answer?.
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