The curve passing through the point (1,1...

The curve passing through the point `(1,1)` satisfies the differential equation `(dy)/(dx)+(sqrt((x^2-1)(y^2-1)))/(x y)=0` . If the curve passes through the point `(sqrt(2),k),` then the value of `[k]` is (where [.] represents greatest integer function)_____

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