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MHT CET202313 May 2023Evening ShiftMathematicsApplication of DerivativesActual

If slope of the tangent to the curve x y+a x+b y=0 at the point (1,1) on it is 2 , then the value of 3 a+b is (

Options

  1. A3
  2. B1
  3. C2
  4. D-1

Correct answer

B. 1

Step-by-step solution

x y+a x+b y=0 Differentiating w.r.t. x , we get x ~d y ~d x +y+ a + b d y ~d x =0 aligned & d y ~d x =- a +y ~b +x & ( d y ~d x )_ ( b , 1) =- a +1 ~b +1 & 2=- a +1 ~b +1 aligned a+2 b=-3 ...(i) Also, the point (1,1) lies on the curve x y+a x+b y=0 . 1+a+b=0 a+b=-1 ...(ii) Solving (i) and (ii), we get a=1, b=-2 3 a+b=1

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