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Class 12 Continuity And Differentiability · Short Answer2 Marksparametric_derivatives

Class 12 Maths · Continuity And Differentiability · Short Answer #119

For x=\(10 t - 10 \sin{\left(t \right)}\), y=\(12 - 12 \cos{\left(t \right)}\), find dy/dx at t=\(\frac{2 \pi}{3}\). Assume dx/dt≠0.

✅ Step-by-Step Solution

Final Answer: \(\frac{2 \sqrt{3}}{5}\)
  1. Differentiate in t: dx/dt=\(10 - 10 \cos{\left(t \right)}\) and dy/dt=\(12 \sin{\left(t \right)}\).
  2. Thus dy/dx=(dy/dt)/(dx/dt)=\(\frac{12 \sin{\left(t \right)}}{10 - 10 \cos{\left(t \right)}}\).
  3. Therefore dy/dx=\(\frac{2 \sqrt{3}}{5}\).

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] Differentiate in t: dx/dt=\(10 - 10 \cos{\left(t \right)}\) and dy/dt=\(12 \sin{\left(t \right)}\).
  • [1 mark] Thus dy/dx=(dy/dt)/(dx/dt)=\(\frac{12 \sin{\left(t \right)}}{10 - 10 \cos{\left(t \right)}}\).
  • [0.5 marks] Therefore dy/dx=\(\frac{2 \sqrt{3}}{5}\).

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