Consider (0, b) as the point on the y-axis whose distance from line

\( \dfrac{x}{3}+\dfrac{y}{4}=1\) is 4 units.

It can be written as 4x + 3y – 12 = 0 ……. (1)

By comparing equation (1) to the general equation of line Ax + By + C = 0, we get

A = 4, B = 3 and C = – 12

We know that the perpendicular distance (d) of a line Ax + By + C = 0 from (x_{1}, y_{1}) is written as

\(4=|\dfrac{4(0)+3(b)-12}{\sqrt{4^2+3^2}}|\)

\( 4=|\dfrac{3b-12}{5}|\)

By cross multiplication

20 = |3b – 12|

We get

20 = ± (3b – 12)

Here 20 = (3b – 12) or 20 = – (3b – 12)

It can be written as

3b = 20 + 12 or 3b = -20 + 12

So we get

b = \( \dfrac{32}{3}\)or b = \(- \dfrac{8}{3}\)

Hence, the required points are (0,\( \dfrac{32}{3}\)) and (0, \( - \dfrac{8}{3}\)).

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