If a circle passes through the points where the lines `3kx- 2y-1 = 0` and `4x-3y + 2 = 0` meet the coordinate axes then `k=`

Options

A. 1
B. `-1`
C. `(1)/(2)`
D. `(-1)/(2)`

Answer

C

Explanation

The line `3kx -2y -1 =0` meets x-axis and y-axis at `A ((1)/(3k),0)` and `B(0,-(1)/(2))`, respectively. Also, the line `4x -3y +2 =0` cuts x-axis and y-axis at `C(-(1)/(2),0)` and `D(0,(2)/(3))`, respectively.

Since the four points are concyclic, we have
`OBxx OD +OA xx OC`
`rArr (1//2)(2//3) = (1//3) (1//2)`
`rArr k =1//2`