Find the points on x-axis whose perpendicular distance from the line `3x-4y-12=0` is 3.`

Explanation

Let the required point be `P(x,0)`
Now, Length of perpendicular from `P(a,0)on 3x-4y-12=0is 3.`
`therefore|(3(a)-(0)-12)/(sqrt(3^(2))+4^(2))=3`
`=|(3a-12)/(5)|=3`
`implies|3a-12|=15`
`implies3a-12=+-15`
`implies3a-12=15`
`or 3a-12=-15`
`implies3a =27`
`or 3a=-3`
`impliesa=9`
or `a=-1`
`therefore` The required points are `(9,0)and (-1,0)`