The differential equation for all the straight lines which are at a unit distance from the origin is
1
\({\left( {y - x\frac{{dy}}{{dx}}} \right)^2} = 1 - {\left( {\frac{{dy}}{{dx}}} \right)^2}\)
2
\({\left( {y + x\frac{{dy}}{{dx}}} \right)^2} = 1 + {\left( {\frac{{dy}}{{dx}}} \right)^2}\)
3
\({\left( {y - x\frac{{dy}}{{dx}}} \right)^2} = 1 + {\left( {\frac{{dy}}{{dx}}} \right)^2}\)
4
\({\left( {y + x\frac{{dy}}{{dx}}} \right)^2} = 1 - {\left( {\frac{{dy}}{{dx}}} \right)^2}\)