The equation of line passing through the intersection of 2x+y−4=0 and 2x+y−4=0 is. (2x+y−4)+λ(x−3y+5)=0 x(2+λ)+y(1−3λ)+5λ=0 ......(I) This is at a distance of √5 units from the origin. |
5λ−4
√(2+λ)2+(1−3λ)2
|=√5
(5λ−4)2
4+λ2+4λ+1+9λ2−6λ
=5 25λ2+30λ+9=0 On solving the above we get, λ=−
3
5
Substituting the value of λ in equation (I) we get. (2x+y−4)+−