The solution of differential equation dydx=1−y2y determines family of circles with

We have, dydx=1−y2y∣ On integrating both  sides  we get ∫y1−y2dy=∫dx⇒−12∫−2y1−y2dy=∫dx⇒−1−y2=x+c On squaring both sides, we get (x+c)2+y2=1Which is the equation of circle whose fixed radius is 1 and centre is variable on x- axis