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 at a distance 2 unit from the origin has the equation

x = 2

3x + y – 1 = 0

y = 1

None of these
medium
Solution
x = 2
Any line through the intersection of the given line is
P + λQ = 0
or (x – 3y +1) + λ(2x + 5y – 9) = 0
Its slope will be infinite if it is perpendicular to xaxis i.e. parallel to yaxis.
Hence the coefficient of y will be zero.
or .
Putting for λ the line is x = 2 clearly its distance from (0, 0) is 2.
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