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

straight line having infinite slope is parallel to Y-axis , And is given as x=k where k is distance from the origin.

And the point of intersection of the lines is x=2 and y=1.

and the line is (y-y₁)= m (x-x₁)

= x-2=0

= x=2 is the required straight line equation.