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A line L is perpendicular to the line 3x...

A line `L` is perpendicular to the line `3x-4y-7=0` and touches the circle `x^(2)+y^(2)-2x-4y-4=0`, the `y`-intercept of the line `L` can be:

A

`25/3`

B

`20/3`

C

`17/3`

D

`4/3`

Text Solution

Verified by Experts

The correct Answer is:
A
Line perpendicular to `3x-4y-7=0` is `4x+3y+lamda=0` ………(1)
`CP=3`
`(|4+6+lamda|)/(sqrt(25))=3implies|10+lamda|=15`
Line `L` can be
`4x+3y+5=0` or `4x+3y-25=0`
`y=-4/3x-5/3` or `4x+3y-25=0`
`y=-4/3x-5/3` or `y=-4/3x+25/3`
`:.` possible intercept on `y`-axis are `-5/3x+25/3`
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Knowledge Check

  • If the line 3x-4y-k=0 , touches the circle x^(2)+y^(2)-4x-8y-5=0 at (a,b) , then k+a+b is equal to

    A
    20
    B
    22
    C
    `-30`
    D
    `-28`

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