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JEE Main2015MathematicsApplication of DerivativesActual

The equation of a normal to the curve, sin ⁡ y = x sin ⁡ π 3 + y at x = 0 , is:

Options

  1. A2 x - 3 y = 0
  2. B2 y - 3 x = 0
  3. C2 y + 3 x = 0
  4. D2 x + 3 y = 0

Correct answer

D. 2 x + 3 y = 0

Step-by-step solution

sin ⁡ y = x sin ⁡ π 3 + y If x = 0 ,  then y = 0 So point is 0 ,   0 Slope of tangent = d y d x = + sin ⁡ π 3 + y cos ⁡ y - x cos ⁡ π 3 + y at 0 ,   0 d y d x = sin ⁡ π 3 = 3 2 Slope of tangent = 3 2 Slope of Normal = - 2 3 ∴  equation of normal 2 x + 3 y = 0

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