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if the curve y = ax and y = bx intersect at an angle k then, tan(k)=(a) [ a - b ]/ 1+a b(b) [log a - log b] / [1+ log a . log b](c) [ a+ b]/ 1- a b(d) [ log a + log b]/ [1- log a . log b]
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if the curve y = ax and y = bx intersect at an angle k then, tan(k)=(a...
Intersection of Curves
The curves defined by the equations y = ax and y = bx intersect at specific points, and the angle of intersection can be derived using their slopes.
Slopes of the Curves
- For the curve y = ax, the slope (m1) is a.
- For the curve y = bx, the slope (m2) is b.
Formula for Angle of Intersection
The angle (k) between two intersecting curves can be calculated using the formula:
- tan(k) = |(m1 - m2) / (1 + m1 * m2)|
Substituting the slopes, we have:
- tan(k) = |(a - b) / (1 + ab)|
This indicates that option (a) is the correct representation of the angle of intersection.
Other Options Explained
- Option (b): [log a - log b] / [1 + log a * log b] does not represent the angle of intersection based on the slopes of the linear functions provided.
- Option (c): [a + b] / (1 - ab) does not apply here, as it does not fit the derived formula for the angle between two lines.
- Option (d): [log a + log b] / [1 - log a * log b] similarly does not align with the angle calculation.
Conclusion
The angle of intersection k between the curves y = ax and y = bx is correctly given by:
- tan(k) = (a - b) / (1 + ab)
Thus, the correct answer is option (a).
The curves defined by the equations y = ax and y = bx intersect at specific points, and the angle of intersection can be derived using their slopes.
Slopes of the Curves
- For the curve y = ax, the slope (m1) is a.
- For the curve y = bx, the slope (m2) is b.
Formula for Angle of Intersection
The angle (k) between two intersecting curves can be calculated using the formula:
- tan(k) = |(m1 - m2) / (1 + m1 * m2)|
Substituting the slopes, we have:
- tan(k) = |(a - b) / (1 + ab)|
This indicates that option (a) is the correct representation of the angle of intersection.
Other Options Explained
- Option (b): [log a - log b] / [1 + log a * log b] does not represent the angle of intersection based on the slopes of the linear functions provided.
- Option (c): [a + b] / (1 - ab) does not apply here, as it does not fit the derived formula for the angle between two lines.
- Option (d): [log a + log b] / [1 - log a * log b] similarly does not align with the angle calculation.
Conclusion
The angle of intersection k between the curves y = ax and y = bx is correctly given by:
- tan(k) = (a - b) / (1 + ab)
Thus, the correct answer is option (a).
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if the curve y = ax and y = bx intersect at an angle k then, tan(k)=(a) [ a - b ]/ 1+a b(b) [log a - log b] / [1+ log a . log b](c) [ a+ b]/ 1- a b(d) [ log a + log b]/ [1- log a . log b] for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about if the curve y = ax and y = bx intersect at an angle k then, tan(k)=(a) [ a - b ]/ 1+a b(b) [log a - log b] / [1+ log a . log b](c) [ a+ b]/ 1- a b(d) [ log a + log b]/ [1- log a . log b] covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for if the curve y = ax and y = bx intersect at an angle k then, tan(k)=(a) [ a - b ]/ 1+a b(b) [log a - log b] / [1+ log a . log b](c) [ a+ b]/ 1- a b(d) [ log a + log b]/ [1- log a . log b].
if the curve y = ax and y = bx intersect at an angle k then, tan(k)=(a) [ a - b ]/ 1+a b(b) [log a - log b] / [1+ log a . log b](c) [ a+ b]/ 1- a b(d) [ log a + log b]/ [1- log a . log b] for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about if the curve y = ax and y = bx intersect at an angle k then, tan(k)=(a) [ a - b ]/ 1+a b(b) [log a - log b] / [1+ log a . log b](c) [ a+ b]/ 1- a b(d) [ log a + log b]/ [1- log a . log b] covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for if the curve y = ax and y = bx intersect at an angle k then, tan(k)=(a) [ a - b ]/ 1+a b(b) [log a - log b] / [1+ log a . log b](c) [ a+ b]/ 1- a b(d) [ log a + log b]/ [1- log a . log b].
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