Let $$\lceil$$ denote a curve y = y(x) which is in the first quadrant and let the point (1,0) lie on it. Let the tangent to $$\lceil$$ at a point P intersect the y-axis at $$Y_P$$. If $$PY_P$$ has length 1 for each point P on $$\lceil$$ then which of the following options is/are correct?

A

$$y = \log_e \left(\frac{1 + \sqrt {1 - x^2}}{x}\right) - \sqrt {1 - x^2}$$

B

$$xy' + \sqrt {1 - x^2} = 0$$

C

$$y = -\log_e \left(\frac{1 + \sqrt {1 - x^2}}{x}\right) + \sqrt {1 - x^2}$$

D

$$xy' - \sqrt {1 - x^2} = 0$$