Question

Differential equation for all straight line, which are at a unit distance from the origin?

Answer 1

Answer

The equation of line is y=1or3x−4y−5=0

The equation of line passing through (3,1) is y−1=m(x−3)

Or mx−y−3m+1=0 .

The distance of the origin(0,0)

from the straight line is 1. We know distance of a point

(x0,y0) from a straight line ax+by+c=0 is

d=|ax0+by0+c|√a2+b2 

, here

a=m;b=−1,c=−3m+1,d=1,x0=0,y0=0

∴1=|m⋅0+(−1)⋅0+(−3m+1)|√m2+1

(−3m+1)=√m2+1or(−3m+1)2=m2+1or

9m2−6m+1=m2+1or8m2−6m=0or

m(8m−6)=0∴m=0orm=68=34

The equation of line is when m=0;y=1 and

the equation of line is when m=