Find the foci of the conic passing through the point \( (1,0) \) and satisfying the diffrential ...

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Find the foci of the conic passing through the point \( (1,0) \) and satisfying the diffrential equation \( \left(1+y^{2}\right) d x-x y d y=0 \). Find also the equation of a circle touching the conic at \( \sqrt{2}, 1 \) and passing through one of its foci.
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