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The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 is
- a)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0
- b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0
- c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0
- d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0
Correct answer is option 'C'. Can you explain this answer?
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The equation of the bisectors of the angles between the lines represe...
To find the equation of the bisectors of the angles between the lines represented by the given equation, we can follow these steps:
1. Rewrite the given equation in the standard form of a conic section:
2(x - 2)^2 + 3(x - 2)(y - 2) - 2(y - 2)^2 = 0
2. Simplify the equation by expanding and combining like terms:
2(x^2 - 4x + 4) + 3(x - 2)(y - 2) - 2(y^2 - 4y + 4) = 0
2x^2 - 8x + 8 + 3xy - 6x - 6y + 12 - 2y^2 + 8y - 8 = 0
2x^2 + xy - 14x - y^2 + 2y + 12 = 0
3. Identify the coefficients of x^2, xy, y^2, x, y, and the constant term:
Coefficient of x^2: 2
Coefficient of xy: 1
Coefficient of y^2: -1
Coefficient of x: -14
Coefficient of y: 2
Constant term: 12
4. Use the formula to find the equation of the bisectors:
The equation of the bisectors of the angles between the lines is given by:
(a - b)x^2 - 2hxy + (a + b)y^2 + 2gx + 2fy + c = 0
where a = coefficient of x^2, b = coefficient of y^2, h = coefficient of xy, g = coefficient of x, f = coefficient of y, and c = constant term.
Plugging in the values, we get:
(2 - (-1))x^2 - 2(0)xy + (2 + (-1))y^2 + 2(-14)x + 2(2)y + 12 = 0
3x^2 - 3y^2 - 28x + 4y + 12 = 0
Therefore, the equation of the bisectors of the angles between the lines represented by the given equation is:
3x^2 - 3y^2 - 28x + 4y + 12 = 0
Hence, the correct answer is option 'C': 3x^2 - 3y^2 - 28x + 4y + 12 = 0.
1. Rewrite the given equation in the standard form of a conic section:
2(x - 2)^2 + 3(x - 2)(y - 2) - 2(y - 2)^2 = 0
2. Simplify the equation by expanding and combining like terms:
2(x^2 - 4x + 4) + 3(x - 2)(y - 2) - 2(y^2 - 4y + 4) = 0
2x^2 - 8x + 8 + 3xy - 6x - 6y + 12 - 2y^2 + 8y - 8 = 0
2x^2 + xy - 14x - y^2 + 2y + 12 = 0
3. Identify the coefficients of x^2, xy, y^2, x, y, and the constant term:
Coefficient of x^2: 2
Coefficient of xy: 1
Coefficient of y^2: -1
Coefficient of x: -14
Coefficient of y: 2
Constant term: 12
4. Use the formula to find the equation of the bisectors:
The equation of the bisectors of the angles between the lines is given by:
(a - b)x^2 - 2hxy + (a + b)y^2 + 2gx + 2fy + c = 0
where a = coefficient of x^2, b = coefficient of y^2, h = coefficient of xy, g = coefficient of x, f = coefficient of y, and c = constant term.
Plugging in the values, we get:
(2 - (-1))x^2 - 2(0)xy + (2 + (-1))y^2 + 2(-14)x + 2(2)y + 12 = 0
3x^2 - 3y^2 - 28x + 4y + 12 = 0
Therefore, the equation of the bisectors of the angles between the lines represented by the given equation is:
3x^2 - 3y^2 - 28x + 4y + 12 = 0
Hence, the correct answer is option 'C': 3x^2 - 3y^2 - 28x + 4y + 12 = 0.
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The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. Can you explain this answer?
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The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. 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 equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. 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 equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. Can you explain this answer?.
The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. 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 equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. 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 equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. Can you explain this answer?.
Solutions for The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. Can you explain this answer?, a detailed solution for The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The equation of the bisectors of the angles between the lines represented by the equation 2(x + 2)2 + 3(x + 2)(y - 2) -2(y - 2)2 = 0 isa)3x2 − 8xy − 3y2 − 28x + 4y + 32 = 0b)3x2 + 8xy − 3y2 + 28x − 4y + 32 = 0c)3x2 − 8xy − 3y2 + 28x − 4y + 32 = 0d)3x2 − 8xy − 3y2 + 28x − 4y − 32 = 0Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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