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The acute angle between the lines x – y = 0 and y = 0 is
- a)450
- b)750
- c)300
- d)600
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The acute angle between the lines x – y = 0 and y = 0 isa)450b)7...
It's clearly seen one line is perpendicular to x axis and another is made 45 degree with x axis
so angle between them is 45 degree
so angle between them is 45 degree
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The acute angle between the lines x – y = 0 and y = 0 isa)450b)7...
Understanding the Lines
The lines given are:
- Line 1: \( x - y = 0 \) (which can be rewritten as \( y = x \))
- Line 2: \( y = 0 \) (the x-axis)
Calculating Slopes
- The slope of Line 1 (\( y = x \)) is \( m_1 = 1 \).
- The slope of Line 2 (\( y = 0 \)) is \( m_2 = 0 \).
Using the Angle Formula
To find the acute angle (\( \theta \)) between two lines, we use the formula:
\[
\tan(\theta) = \left| \frac{m_1 - m_2}{1 + m_1 \cdot m_2} \right|
\]
Substituting the values:
\[
\tan(\theta) = \left| \frac{1 - 0}{1 + 1 \cdot 0} \right| = \left| \frac{1}{1} \right| = 1
\]
Finding the Angle
The angle \( \theta \) whose tangent is 1 is:
\[
\theta = 45^\circ
\]
Since we need the acute angle between the lines, we confirm that \( 45^\circ \) is indeed acute.
Conclusion
Thus, the acute angle between the lines \( x - y = 0 \) and \( y = 0 \) is \( 45^\circ \), making the correct answer option ‘A’.
The lines given are:
- Line 1: \( x - y = 0 \) (which can be rewritten as \( y = x \))
- Line 2: \( y = 0 \) (the x-axis)
Calculating Slopes
- The slope of Line 1 (\( y = x \)) is \( m_1 = 1 \).
- The slope of Line 2 (\( y = 0 \)) is \( m_2 = 0 \).
Using the Angle Formula
To find the acute angle (\( \theta \)) between two lines, we use the formula:
\[
\tan(\theta) = \left| \frac{m_1 - m_2}{1 + m_1 \cdot m_2} \right|
\]
Substituting the values:
\[
\tan(\theta) = \left| \frac{1 - 0}{1 + 1 \cdot 0} \right| = \left| \frac{1}{1} \right| = 1
\]
Finding the Angle
The angle \( \theta \) whose tangent is 1 is:
\[
\theta = 45^\circ
\]
Since we need the acute angle between the lines, we confirm that \( 45^\circ \) is indeed acute.
Conclusion
Thus, the acute angle between the lines \( x - y = 0 \) and \( y = 0 \) is \( 45^\circ \), making the correct answer option ‘A’.
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The acute angle between the lines x – y = 0 and y = 0 isa)450b)750c)300d)600Correct answer is option 'A'. Can you explain this answer?
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The acute angle between the lines x – y = 0 and y = 0 isa)450b)750c)300d)600Correct 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 The acute angle between the lines x – y = 0 and y = 0 isa)450b)750c)300d)600Correct 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 The acute angle between the lines x – y = 0 and y = 0 isa)450b)750c)300d)600Correct answer is option 'A'. Can you explain this answer?.
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