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

$\begin{array}{l}\text{ We have, }\frac{dy}{dx}=\frac{\sqrt{1-y^2}}{y}\mid \\ \text{ On integrating both sides }\\ \text{ we get }\int \frac{y}{\sqrt{1-y^2}}dy=\int dx\\ \Rightarrow -\frac{1}{2}\int \frac{-2y}{\sqrt{1-y^2}}dy=\int dx\\ \Rightarrow -\sqrt{1-y^2}=x+c\end{array}$

$\text{ On squaring both sides, we get }(x+c{)}^2+y^2=1$

Which is the equation of circle whose fixed radius is 1 and centre is variable on $x-$ axis