Question

The straight line passing through the point of intersection of the straight lines
$x-3y+1=0$ and $2x+5y-9=0$
and having infinite slope and and at a distance 2 units from the origin has the equation

• A. $x=2$
• B. $3x+y-1=0$
• C. $y=1$
• D. None of these

Answer 1

The correct option is A $x=2$

Any line through the intersection of given lines is $P+\lambda Q=0$
or $(x-3y+1)+\lambda (2x+5y-9)=0$
Its slope will be infinite if it is perpendicular to x-axis i.e. parallel to y-axis.
Hence the coefficient of $y$ will be zero.
$\therefore -3+5y=0$
or $\lambda =3/5$. Putting for $\lambda$ the line is $x-2=0$. Clearly its distance from $(0,0)$ is 2.