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MHT CET202519 Apr 2025Morning ShiftMathematicsApplication of DerivativesActual

The angle between the curves x y =6 and x^2 y =12 is

Options

  1. A⁻¹ 3 11
  2. B⁻¹ 11 3
  3. C⁻¹ 2 11
  4. D⁻¹ 1 11

Correct answer

A. ⁻¹ 3 11

Step-by-step solution

The angle between two curves corresponds to the angle between their tangents at the point of intersection. The point of intersection satisfies both xy = 6 and x^2y = 12 . Substituting y = 6 x from the first equation into the second gives x^2( 6 x ) = 12 , simplifying to 6x = 12 and x = 2 . The corresponding y -value is 6 2 = 3 , yielding the intersection point (2,3) . Differentiating xy = 6 implicitly gives y + x dy dx = 0 , so dy dx = - y x . At (2,3) the slope is m₁ = - 3 2 . For x^2y = 12 , implicit differentiat

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