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MHT CET20239 May 2023Evening ShiftMathematicsApplication of DerivativesActual

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

Options

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

Correct answer

A. 3

Step-by-step solution

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

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