AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper

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)+−

3

5

(x−3y+5)=0
7x+14y−35=0
x+2y−5=0