The differential equation $$\frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{y}$$ determines a family of circles with

A

variable radii and a fixed centre at (0, 1)

B

variable radii and a fixed centre at (0, -1)

C

fixed radius 1 and variable centres along the x-axis

D

fixed radius 1 and variable centres along the y-axis