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Solution :

`(x)/(3)-(y)/(4)=1 Rightarrow 4x-3y-12=0........(i)` <br> Let P(0,y) be a point on the y-aixs whose perpendicular distance from the line 4x-3y-12=0 is 3 units. Then, <br> `(|4xx0-3y-12|)/(sqrt(4^(2)+(-3)^(2)))=3 Rightarrow |-3y-12|=15 Rightarrow |-3(y+4)|=15` <br> `Rightarrow |-(y+4)|=5 Rightarrow |y+4|=5` <br> `Rightarrow |(y+4=5)| or (y+4=-5)` <br> `Rightarrow y=1 or y=-9` <br> `Rightarrow y=1 or y=-9` <br> Hence, the required points are (0,1) and (0,-9)