Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?

[c] y=mx+c (Equation of straight lie) dydx=m and mx−y+c=0 is at unit distance from origin. ∴|m(0)−(0)+c|m2+(−1)2−−−−−−−−−√=1⇒c=1+m2−−−−−−√ Now: [y−xdydx]2=[mx+c−xm]2=c2=1+m2 also, [y+xdydx]2=[mx+c+mx]2=[2mx+1+m2−−−−−−√]2 also, 1−(dydx)2=1−m2 and 1+(dydx)2=1+m2 ⇒[y−xdydx]2=1+(dydx)2