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let T denote a curve y=f(x) which is in ...

let T denote a curve `y=f(x)` which is in the first quadrant and let the point (1,0) lie on it. Let the tangent to T at a point P intersect the y-axis at `Y_(P)` and `PY_P` has length 1 for each poinit P on T. then which of the following option may be correct?

A

`y=log_(e)((1+sqrt(1-x^2))/(x))-sqrt(1-x^2)`

B

`xy'+sqrt(1+x^2)=0`

C

`y= - log_(e)((1+sqrt(1-x^2))/(x))+sqrt(1-x^2)`

D

`xy'-sqrt(1-x^2)=0`

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