Differential Equations

Statement I The differential equation corresponding to the family of circles having their centres on $Y$-axis and fixed radius $k$ is $\left(x^2-k^2\right)\left(\frac{d y}{d x}\right)^2+x^2=0$

Statement II The differential equation corresponding to the family of circles passing through the origin and having their centres on $X$-axis is $x^2-y^2+2 x y \frac{d y}{d x}=0$

Which of the above statements is (are) true?