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If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t < π/2, with the positive x-axis is π/3, then y0 is equal to:
- a)6(3 + 2√2)
- b)3(7 + 4√3)
- c)27
- d)48
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the angle made by the tangent at the point (x0, y0) on the curve x ...
To find the angle made by the tangent at the point (x0, y0) on the curve, we need to find the slope of the tangent at that point.
Given the parametric equations:
x = 12(t - sin t cos t)
y = 12(1 - sin^2 t)
Differentiating both equations with respect to t, we get:
dx/dt = 12(1 - cos^2 t) - 12(cos^2 t - sin^2 t)
= 12 - 24cos^2 t
dy/dt = -24sin t cos t
To find the slope of the tangent at point (x0, y0), we substitute t0 into the derivatives:
dx/dt |t=t0 = 12 - 24cos^2 t0
dy/dt |t=t0 = -24sin t0 cos t0
The slope of the tangent is given by dy/dx, so we divide the two derivatives:
dy/dx = (dy/dt) / (dx/dt)
= (-24sin t0 cos t0) / (12 - 24cos^2 t0)
To find the angle made by the tangent, we take the inverse tangent of the slope:
angle = arctan(dy/dx)
= arctan[(-24sin t0 cos t0) / (12 - 24cos^2 t0)]
Given the parametric equations:
x = 12(t - sin t cos t)
y = 12(1 - sin^2 t)
Differentiating both equations with respect to t, we get:
dx/dt = 12(1 - cos^2 t) - 12(cos^2 t - sin^2 t)
= 12 - 24cos^2 t
dy/dt = -24sin t cos t
To find the slope of the tangent at point (x0, y0), we substitute t0 into the derivatives:
dx/dt |t=t0 = 12 - 24cos^2 t0
dy/dt |t=t0 = -24sin t0 cos t0
The slope of the tangent is given by dy/dx, so we divide the two derivatives:
dy/dx = (dy/dt) / (dx/dt)
= (-24sin t0 cos t0) / (12 - 24cos^2 t0)
To find the angle made by the tangent, we take the inverse tangent of the slope:
angle = arctan(dy/dx)
= arctan[(-24sin t0 cos t0) / (12 - 24cos^2 t0)]
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If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t < π/2, with the positive x-axis is π/3, then y0 is equal to:a)6(3 + 2√2)b)3(7 + 4√3)c)27d)48Correct answer is option 'C'. Can you explain this answer?
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If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t < π/2, with the positive x-axis is π/3, then y0 is equal to:a)6(3 + 2√2)b)3(7 + 4√3)c)27d)48Correct answer is option 'C'. 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 If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t < π/2, with the positive x-axis is π/3, then y0 is equal to:a)6(3 + 2√2)b)3(7 + 4√3)c)27d)48Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t < π/2, with the positive x-axis is π/3, then y0 is equal to:a)6(3 + 2√2)b)3(7 + 4√3)c)27d)48Correct answer is option 'C'. Can you explain this answer?.
If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t < π/2, with the positive x-axis is π/3, then y0 is equal to:a)6(3 + 2√2)b)3(7 + 4√3)c)27d)48Correct answer is option 'C'. 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 If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t < π/2, with the positive x-axis is π/3, then y0 is equal to:a)6(3 + 2√2)b)3(7 + 4√3)c)27d)48Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the angle made by the tangent at the point (x0, y0) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)2, 0 < t < π/2, with the positive x-axis is π/3, then y0 is equal to:a)6(3 + 2√2)b)3(7 + 4√3)c)27d)48Correct answer is option 'C'. Can you explain this answer?.
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