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Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .
Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.
Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.
- a)Statement -1 is false, Statement-2 is true
- b)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
- c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
- d)Statement -1 is true, Statement-2 is false
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = ...
The equation represents a pair of lines if 1×1×4 + 2× f ×g×1-1×f 2 -1×g 2 - 4×12 = 0
⇒ (f - g) 2 = 0 ⇒ f=g
The equation becomes (x + y)2 + 2g(x + y) + 4 = 0 Which represents pair of parallel lines, which are real provided (2g) 2 - 4 × 4 ×1 > 0 Þ| g | > 2.
⇒ (f - g) 2 = 0 ⇒ f=g
The equation becomes (x + y)2 + 2g(x + y) + 4 = 0 Which represents pair of parallel lines, which are real provided (2g) 2 - 4 × 4 ×1 > 0 Þ| g | > 2.
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Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = ...
= | f |
Statement-2 : The angle between the pair of lines represented by the general equation ax2 2hxy by2 2gx 2fy c = 0 is given by tan 2θ = 2h / (a - b)
Statement-1 is true.
Explanation: The given general equation can be written as (x + y)2 + (2g - x2 - y2) = 0. For a pair of real lines, the discriminant of this equation should be greater than or equal to 0. Therefore, 4g2 - 4(1)(2g - x2 - y2) = 8(x2 + y2 - g) ≥ 0. This implies that | g | ≤ √2(x2 + y2), which further implies that | g | ≤ | f | (since f2 = g(x2 + y2)).
Statement-2 is also true.
Explanation: The given equation can be written as (x - y)2 + (2gx + 2fy - c) = 0. The lines represented by this equation have slope m = tan θ, where θ is the angle between them. Therefore,
m = tan θ = ±√(2h / (a - b))
(± sign depends on whether the lines are real or imaginary). Taking tangent on both sides and simplifying, we get the required expression.
Statement-2 : The angle between the pair of lines represented by the general equation ax2 2hxy by2 2gx 2fy c = 0 is given by tan 2θ = 2h / (a - b)
Statement-1 is true.
Explanation: The given general equation can be written as (x + y)2 + (2g - x2 - y2) = 0. For a pair of real lines, the discriminant of this equation should be greater than or equal to 0. Therefore, 4g2 - 4(1)(2g - x2 - y2) = 8(x2 + y2 - g) ≥ 0. This implies that | g | ≤ √2(x2 + y2), which further implies that | g | ≤ | f | (since f2 = g(x2 + y2)).
Statement-2 is also true.
Explanation: The given equation can be written as (x - y)2 + (2gx + 2fy - c) = 0. The lines represented by this equation have slope m = tan θ, where θ is the angle between them. Therefore,
m = tan θ = ±√(2h / (a - b))
(± sign depends on whether the lines are real or imaginary). Taking tangent on both sides and simplifying, we get the required expression.
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Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer?
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Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. 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 Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer?.
Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. 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 Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Statement-1 : If the general equation x2 + y2 + 2xy + 2gx + 2fy + 4 = 0 represents a pair of real lines then | g |>2 .Statement-2 : The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 represents pair of real lines if abc + 2fgh – af2 – bg2 – ch2 = 0.a)Statement -1 is false, Statement-2 is trueb)Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1c)Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1d)Statement -1 is true, Statement-2 is falseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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