The order of the differential equation of all parabolas,whose latus rectum is $4a$ and axis is parallel to the $x$-axis,is

If $m$ and $n$ are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and $X$-axis as its axis,then $m n-m+n=$

The differential equation of all parabolas with axis parallel to the $y$-axis is

The differential equation formed by eliminating $a$ and $b$ from the equation $y=e^x(a \cos x+b \sin x)$ is

Statement $I$: The differential equation corresponding to the family of circles having their centres on $Y$-axis and fixed radius $k$ is $(x^2-k^2)(\frac{dy}{dx})^2+x^2=0$.
Statement $II$: The differential equation corresponding to the family of circles passing through the origin and having their centres on $X$-axis is $x^2-y^2+2xy \frac{dy}{dx}=0$.
Which of the above statements is (are) true?

Form the differential equation of the family of circles touching the $x$-axis at the origin.