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

Answer

(0,1) and (0,9)

Explanation

Let the required point be `P(0, alpha)`. It is given that the length of the perpendicular from `P(0, alpha)` on 4x-3y-12=0 is 3. Therefore,
`|(4(0)-3alpha-12)/(sqrt(4^(2)+(-3)^(2)))|=3`
`"or " |3alpha+12| = 15`
`"or " |alpha+4| = 5`
`"or " alpha+4 =+-5`
`"or " alpha = 1, -9`
Hence, the required points are (0,1) and (0,-9).