AP ICET 2017 Shift 1 Paper

         $2\mathit{x}+5\mathit{y}=9$
         $\mathit{x}-3\mathit{y}=-1]\times 2$
         –––––––––––––––
Subtracting we get   $11\mathit{y}=11$
Substituting in second equation we get
$\mathit{x}=\mathit{–}1+3\Rightarrow \mathit{x}=2$
Point of intersection is (2, 1)
We can write equation of line as
$\mathit{y}\mathit{–}1=\mathit{m}\left(\mathit{x}\mathit{–}2\right)\Rightarrow \mathit{y}\mathit{–}1=\mathit{m}\mathit{x}\mathit{–}2\mathit{m}$
$\Rightarrow \mathit{m}\mathit{x}\mathit{–}\mathit{y}+\left(1\mathit{–}2\mathit{m}\right)=0$
Writing for distance from origin,
$\Rightarrow 1+4{\mathit{m}}^2-4\mathit{m}=5{\mathit{m}}^2+5$
Equation of line,
$\mathit{y}-1=-2\left(\mathit{x}-2\right)\Rightarrow \mathit{y}-1=-2\mathit{x}+4$
$\Rightarrow 2\mathit{x}+\mathit{y}=5$