The equation of set of lines which are at a constant distance of 2 units from the origin and$\alpha$is angle made by perpendicular from origin is

If normal to the line makes an  angle $\mathrm{\alpha }$ with x-axis, then equation of line is

$\mathrm{xcos\alpha }+\mathrm{ysin\alpha }=\mathrm{p},$ where p is distance of line form origin.

Here, p=2

So,  the equation of line is $\mathrm{xcos\alpha }+\mathrm{ysin\alpha }=2.$