The Differential Equation of all parabolas each of which has latus rectum 4 and whose axis is parallel to the x - axis is

$(y-k{)}^2=4(x-h)$

differentiating w.r.t x we get $2(y-k)y_1=4$

$\Rightarrow \mathrm{k}=\mathrm{y}-\frac{2}{{\mathrm{y}}_1}$, Again differentiating with respect to x,

we get $0=y_1+\frac{2y_2}{{\left(y_1\right)}^2}\Rightarrow 2y_2+{\left(y_1\right)}^3=0$