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If a circle passes through the points wh...

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=`

A

1

B

`-1`

C

`(1)/(2)`

D

`(-1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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