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For what value of 'a' will the lines represented by the equation ax2 - 6xy + 9y2 + 3x - 9y - 4 = 0 be perpendicular?
- a)0
- b)1/2
- c)-9
- d)9
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
For what value of a will the lines represented by the equation ax2- 6x...
Perpendicular Lines:
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if one line has a slope of m, then a line perpendicular to it will have a slope of -1/m.
Finding the Slope:
To find the slope of the given equation ax^2 - 6xy + 9y^2 + 3x - 9y - 4 = 0, we need to rewrite it in the form y = mx + c. Then, the coefficient of x will give us the slope.
Equation in y = mx + c form:
The given equation can be rewritten as 6xy = ax^2 + 9y^2 + 3x - 9y - 4. Dividing by 6 on both sides gives us y = (a/6)x + (3/2)y^2 + (1/2)x - (3/2)y - (2/3).
Finding the Slope:
The coefficient of x in the equation y = (a/6)x + (3/2)y^2 + (1/2)x - (3/2)y - (2/3) is (a/6). For the lines to be perpendicular, the negative reciprocal of this slope should be the slope of the other line.
Negative Reciprocal Slope:
The negative reciprocal of (a/6) is -6/a. Therefore, for the lines to be perpendicular, the slope of the original line should be -6/a.
For Perpendicular Lines:
For the lines to be perpendicular, the slope of the original line should be equal to -6/a. Therefore, a = -6/(-9) = 2/3.
Therefore, the value of a for which the lines represented by the equation ax^2 - 6xy + 9y^2 + 3x - 9y - 4 = 0 will be perpendicular is 2/3.
Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if one line has a slope of m, then a line perpendicular to it will have a slope of -1/m.
Finding the Slope:
To find the slope of the given equation ax^2 - 6xy + 9y^2 + 3x - 9y - 4 = 0, we need to rewrite it in the form y = mx + c. Then, the coefficient of x will give us the slope.
Equation in y = mx + c form:
The given equation can be rewritten as 6xy = ax^2 + 9y^2 + 3x - 9y - 4. Dividing by 6 on both sides gives us y = (a/6)x + (3/2)y^2 + (1/2)x - (3/2)y - (2/3).
Finding the Slope:
The coefficient of x in the equation y = (a/6)x + (3/2)y^2 + (1/2)x - (3/2)y - (2/3) is (a/6). For the lines to be perpendicular, the negative reciprocal of this slope should be the slope of the other line.
Negative Reciprocal Slope:
The negative reciprocal of (a/6) is -6/a. Therefore, for the lines to be perpendicular, the slope of the original line should be -6/a.
For Perpendicular Lines:
For the lines to be perpendicular, the slope of the original line should be equal to -6/a. Therefore, a = -6/(-9) = 2/3.
Therefore, the value of a for which the lines represented by the equation ax^2 - 6xy + 9y^2 + 3x - 9y - 4 = 0 will be perpendicular is 2/3.
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For what value of a will the lines represented by the equation ax2- 6xy + 9y2+ 3x - 9y - 4 = 0 be perpendicular?a)0b)1/2c)-9d)9Correct answer is option 'C'. Can you explain this answer?
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For what value of a will the lines represented by the equation ax2- 6xy + 9y2+ 3x - 9y - 4 = 0 be perpendicular?a)0b)1/2c)-9d)9Correct answer is option 'C'. 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 For what value of a will the lines represented by the equation ax2- 6xy + 9y2+ 3x - 9y - 4 = 0 be perpendicular?a)0b)1/2c)-9d)9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For what value of a will the lines represented by the equation ax2- 6xy + 9y2+ 3x - 9y - 4 = 0 be perpendicular?a)0b)1/2c)-9d)9Correct answer is option 'C'. Can you explain this answer?.
For what value of a will the lines represented by the equation ax2- 6xy + 9y2+ 3x - 9y - 4 = 0 be perpendicular?a)0b)1/2c)-9d)9Correct answer is option 'C'. 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 For what value of a will the lines represented by the equation ax2- 6xy + 9y2+ 3x - 9y - 4 = 0 be perpendicular?a)0b)1/2c)-9d)9Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For what value of a will the lines represented by the equation ax2- 6xy + 9y2+ 3x - 9y - 4 = 0 be perpendicular?a)0b)1/2c)-9d)9Correct answer is option 'C'. Can you explain this answer?.
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