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The equation of a pair of lines passing through origin which make angle α with y = x is
- a)x2+2xy sec2α+y2=0
- b)x2+2xy cosecα+y2=0
- c)x2-2xy cosec2α+y2=0
- d)x2-2xy sec2α+y2=0
Correct answer is option 'D'. Can you explain this answer?
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The equation of a pair of lines passing through origin which make angl...
Let the lines passing through the origin make an angle of $\theta$ with each other. Then we can write the equations of these lines in the slope-intercept form as $y = m_1 x$ and $y = m_2 x$, where $m_1 = \tan\theta$ and $m_2 = \tan(\theta + \pi/2) = -\cot\theta$. Thus, the equations of the lines are $y = \tan\theta\, x$ and $y = -\cot\theta\, x$.
Alternatively, we can use the fact that the sum of the slopes of two perpendicular lines is always equal to $-1$. Since the first line has slope $\tan\theta$, the slope of the second line must be $-\frac{1}{\tan\theta} = -\cot\theta$. Therefore, the equations of the lines are $y = \tan\theta\, x$ and $y = -\cot\theta\, x$.
Alternatively, we can use the fact that the sum of the slopes of two perpendicular lines is always equal to $-1$. Since the first line has slope $\tan\theta$, the slope of the second line must be $-\frac{1}{\tan\theta} = -\cot\theta$. Therefore, the equations of the lines are $y = \tan\theta\, x$ and $y = -\cot\theta\, x$.
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The equation of a pair of lines passing through origin which make angle α with y = x isa)x2+2xy sec2α+y2=0b)x2+2xy cosecα+y2=0c)x2-2xy cosec2α+y2=0d)x2-2xy sec2α+y2=0Correct answer is option 'D'. Can you explain this answer?
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The equation of a pair of lines passing through origin which make angle α with y = x isa)x2+2xy sec2α+y2=0b)x2+2xy cosecα+y2=0c)x2-2xy cosec2α+y2=0d)x2-2xy sec2α+y2=0Correct 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 The equation of a pair of lines passing through origin which make angle α with y = x isa)x2+2xy sec2α+y2=0b)x2+2xy cosecα+y2=0c)x2-2xy cosec2α+y2=0d)x2-2xy sec2α+y2=0Correct 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 The equation of a pair of lines passing through origin which make angle α with y = x isa)x2+2xy sec2α+y2=0b)x2+2xy cosecα+y2=0c)x2-2xy cosec2α+y2=0d)x2-2xy sec2α+y2=0Correct answer is option 'D'. Can you explain this answer?.
The equation of a pair of lines passing through origin which make angle α with y = x isa)x2+2xy sec2α+y2=0b)x2+2xy cosecα+y2=0c)x2-2xy cosec2α+y2=0d)x2-2xy sec2α+y2=0Correct 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 The equation of a pair of lines passing through origin which make angle α with y = x isa)x2+2xy sec2α+y2=0b)x2+2xy cosecα+y2=0c)x2-2xy cosec2α+y2=0d)x2-2xy sec2α+y2=0Correct 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 The equation of a pair of lines passing through origin which make angle α with y = x isa)x2+2xy sec2α+y2=0b)x2+2xy cosecα+y2=0c)x2-2xy cosec2α+y2=0d)x2-2xy sec2α+y2=0Correct answer is option 'D'. Can you explain this answer?.
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