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1)

 The coordinates of a a point on the curve  x=a(θ+sinθ),y=a(1cosθ)   where the tangent is inclined at an angle π4  to the positive X-axis , are


A) (a(π21)a)

B) (a(π2+1)a)

C) (aπ2,a)

D) (a,a)

Answer:

Option B

Explanation:

 According  to the given information,

    dydx=1            ..............(i)

    dydθ=asinθ and dxdθ=a(1+cosθ) 

    dydx=dydθdxdθ=asinθa(1+cosθ)=1

 sinθ1+cosθ=12sinθ2cosθ22cos2θ2=1tanθ2=1

  θ2=π4θ=π2

 So, the required point on the curve is    (a(π2+1)a)

 hence  , option (b) is correct