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MHT CET202620 April 2026Morning ShiftMathematicsApplication of DerivativesActual

If the line ax + by + 5 = 0 is a normal to the curve xy = 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

A. a > 0, b < 0

Step-by-step solution

The equation of the given curve is xy = 1 , which can be written as y = 1 x . Differentiating with respect to x , we get the slope of the tangent: dy dx = - 1 x^2 The slope of the normal to the curve is given by: m = - 1 dy dx = x^2 Since x 0 for any point on the curve xy = 1 , we have x^2 > 0 . Thus, the slope of the normal is always strictly positive. The given equation of the normal is ax + by + 5 = 0 . The slope of this line is - a b . For this line to represent a normal to the curve, its slope must be positive

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