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

Step-by-step solution

y=m x+c (Equation of straight line) d y d x =m and m x-y+c=0 is at unit distance from origin. |m(0)-(0)+c| m^2+(-1)^2 =1 c= 1+m^2 Now: [y-x d y d x ]^2=[m x+c-x m]^2 c^2=1+m^2 also, [y+x d y d x ]^2=[m x+c+m x]^2= [2 m x+ 1+m^2 ]^2 also, 1- ( d y d x )^2=1-m^2 and 1+ ( d y d x )^2=1+m^2 [y-x d y d x ]^2=1+ ( d y d x )^2