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MHT CET202618 April 2026Morning ShiftMathematicsApplication of DerivativesActual

If the tangent to the curve xy + ax + by = 0 at (1,1) makes an angle of ⁻¹2 with positive direction of the x -axis, then the value of ab a+b is...

Options

  1. A1
  2. B-1
  3. C2
  4. D-2

Correct answer

C. 2

Step-by-step solution

Since the point (1,1) lies on the curve xy + ax + by = 0 , substituting x=1 and y=1 gives: 1 + a + b = 0 a + b = -1 Differentiating the equation of the curve with respect to x , we get: y + x dy dx + a + b dy dx = 0 dy dx = - y+a x+b The slope of the tangent at (1,1) is given as ( ⁻¹2) = 2 . . dy dx |_ (1,1) = - 1+a 1+b = 2 -1 - a = 2 + 2b a + 2b = -3 Solving a + b = -1 and a + 2b = -3 , we get: b = -2 and a = 1 The value of ab a+b is: (1)(-2) -1 = 2 Answer: 2

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