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A tangent and a normal to a curve at any...

A tangent and a normal to a curve at any point P meet the x and y axes at A, B and C, D respectively. Find the equation of the curve passing through `(1, 0)` if the centre of circle through `O.C, P and B` lies on the line y = x (where O is the origin).

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`log(sqrt(x^(2) + y^(2))) + tan^(-1) ((y)/(x)) = 0`
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