If lines `x+2y-1=0,a x+y+3=0,` and `b x-y+2=0` are concurrent, and `S` is the curve denoting the locus of `(a , b)` , then the least distance of `S` from the origin is `5/(sqrt(57))` (b) `5//sqrt(51)` `5//sqrt(58)` (d) `5//sqrt(59)`

Options

A. `5//sqrt(57)`
B. `5//sqrt(51)`
C. `5//sqrt(58)`
D. `5//sqrt(59)`

Answer

C

Explanation

The lines are concurrent if
`|{:(1,2,-1),(a,1,3),(b,-1,2):}|=0`
or 7b-3a+5=0
The locus of (a,b) is 3x-7y=5.
Least distance from (0,0) = Length of perpendicular from (0,0)
`=(5)/(sqrt(58))`