The differential equation of the family of circles touching the \(y-\)axis at origin is

\(2xyy^{\prime}+x^2=y^2\) \(2xyy^{\prime}+y^2=x^2\) \(xyy^{\prime}+x^2=y^2\) \(2xyy^{\prime}+2x^2=y^2\)

\(2xyy^{\prime}+x^2=y^2\)

The Center of the given circles lies on the \(x-\)axis. Write equation of circle and proceed to find required equation