We have a continous,differentiable curve passing through \((0,1)\) defined as \(f(x,y)=0\) satisfying the property that the area made by tangent and normal to the curve at any point on the curve \((x,y)\) and the x-axis is equal to the magnitude of the ordinate(i.e. \(=\left| y\right|\) ).

There are exactly two possible curves satisfying the condition. One is bounded and the other one is unbounded curves.

Let the area bounded by the bounded curve and the y-axis be = \(a-\frac{b\pi}{c}\),where \(a,b,c\) are positive integers and \(b,c\) are co-prime.

Find \(a+b+c\)

**Details and assumptions**

1) I am saying unbounded curve in the sense that for some x either y is tending to infinity or for some y,x is tending to infinity.

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