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MHT CET202523 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

If the line a x+ by + c =0 is normal to the curve x y =1 , then

Options

  1. Aa>0, b>0
  2. Ba>0, b < 0
  3. Ca < 0, b 0
  4. Da < 0, b < 0

Correct answer

B. a>0, b < 0

Step-by-step solution

Given the line ax + by + c = 0 is normal to the curve xy = 1 , we determine the required relationship between a and b . Find the derivative of xy = 1 using implicit differentiation: y + x dy dx = 0 , so dy dx = - y x . The slope of the normal is the negative reciprocal of the tangent slope: m_N = x y . The slope of the line ax + by + c = 0 is m_L = - a b . Equating slopes since the line is normal: - a b = x y . On the curve xy = 1 , x and y are non-zero and share the same sign, so x y > 0 . Thus, - a b > 0 , implyi

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