JEE Main2013MathematicsApplication of DerivativesActual

If an equation of a tangent to the curve, y- (x+f),-1-1 x 1+ , is x+2 y=k then k is equal to :

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Correct answer

D. 2

Step-by-step solution

Let y= (x+y) d y d x =- (x+y) (1+ d y d x ) Now, given equation of tangent is aligned &x+2 y=k & Slope = -1 2 aligned So, d y d x = -1 2 put this value in (1), we get aligned & -1 2 =- (x+y) (1- 1 2 ) & (x+y)=1 & x+y= 2 y= 2 -x aligned Now 2 -x= (x+y) x= 2 and y=0 Thus x+2 y=k 2 =k

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