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:

Options

A. `25/3`
B. `20/3`
C. `17/3`
D. `4/3`

Answer

A

Explanation

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`