The differential equation for all the straight lines which are at a unit distance from the origin is

A tangent drawn to the curve $\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)$ at $\mathrm{P}\left(\mathrm{x}, \mathrm{y}\right)$ cuts the $\mathrm{x} \& \mathrm{y}$ axis at $\mathrm{A}$ and $\mathrm{B}$ respectively. If $\mathrm{BP} : \mathrm{AP}=3 : 1$ and $\mathrm{f}\left(1\right)=1$, then tangent to the curve at $\left(1,1\right)$, is