What are the points on the yaxis whose distance from the line `x/3+y/4=1`is 4 units.

Explanation

Let point on `y`-axis is `(0,k)`.
Given line, `(x)/(3)+(y)/(4)=1`
`implies 4x+3y=12implies 4x+3y-12=0`
Length of perpendicular from point `(0,k)` to line `(1)=4`
`implies |(0+3k-12)/(sqrt(4^(2)+3^(2)))|=4`
`implies (3k-12)/(5)=+-4`
`implies 3k-12=+-20`
`implies3k-12=20` or `3k-12=-20`
`implies 3k=32` or `3k=-8`
`implies k=(32)/(3)` or `k=-(8)/(3)`
`:.` Required point `=(0,(32)/(3))` or `(0,(-8)/(3))`