Home
Class 12
MATHS
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`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CIRCLES

    CENGAGE|Exercise Comprehension Type|8 Videos

  • CIRCLE

    CENGAGE|Exercise JEE Advanced (Single Correct Answer Type)|14 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Question Bank|30 Videos

Similar Questions

Explore conceptually related problems

If a circle passes through the point of intersection of the lines x+y+1=0 and x+lambda y-3=0 with the coordinate axis,then value of lambda is

Consider a variable line L which passes through the point of intersection P of the lines 3x+4y=12 and x+2y-5=0 meeting the coordinate axes at points A and B. Then

Knowledge Check

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

    A
    `-1`
    B
    `-1//2`
    C
    `1//2`
    D
    1

  • A variable line passes through the point of intersection of the lines x+2y-1=0 and 2x-y-1=0 and meets the coordinate axes in A and B. The locus of the mid poind of AB is

    A
    `x+3y=0`
    B
    `x+3y=10`
    C
    `x+3y=10xy`
    D
    none

  • If a circle passes through the points of intersection of the lines 2x-y +1=0 and x+lambda y -3=0 with the axes of reference then the value of lambda is :

    A
    `1//2`
    B
    2
    C
    1
    D
    `-2`

    • Similar Questions

    Explore conceptually related problems

    If the lines 2x+3y-1=0 and kx-y+4=0 intersect the coordinate axes in concyclic points then k-1=

    If a circle passes through the points of intersection of the lines 2x-y+1=0 and x+lambda y-3=0 with the axes of reference then the value of lambda is

    Find the equaiton of the circle passing through the point (2, 8), touching the lines 4x-3y-24=0 and 4x+3y-42=0 andhaving x-coordinate of the centre of the circle numerically less than or equal to 8.

    Suppose the lines x-2y+1=0mx+y+3=0' meet the coordinate axes in concyclic points then

    Find the equation of the circle passing through the origin and the points where the line 3x+4y=12 meets the axes of coordinates.

    Home
    Profile