Given:

The condition of line is \[\mathbf{x}/\mathbf{3}\text{ }+\text{ }\mathbf{y}/\mathbf{4}\text{ }=\text{ }\mathbf{1}\]

\[\mathbf{4x}\text{ }+\text{ }\mathbf{3y}\text{ }=\text{ }\mathbf{12}\]

\[\mathbf{4x}\text{ }+\text{ }\mathbf{3y}\text{ }\text{ }\mathbf{12}\text{ }=\text{ }\mathbf{0}\text{ }\ldots \text{ }.\text{ }\left( \mathbf{1} \right)\]

Presently, analyze condition (1) with general condition of line\[\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C}\text{ }=\text{ }\mathbf{0}\] , where \[\mathbf{A}\text{ }=\text{ }\mathbf{4},\text{ }\mathbf{B}\text{ }=\text{ }\mathbf{3},\text{ }\mathbf{and}\text{ }\mathbf{C}\text{ }=\text{ }-\text{ }\mathbf{12}\]

Let (a, 0) be the point on the x-axis, whose separation from the given line is 4 units.

Thus, the opposite distance (d) of a line \[\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C}\text{ }=\text{ }\mathbf{0}\] from a point (x1, y1) is given by

\[\left| \mathbf{4a}\text{ }\text{ }\mathbf{12} \right|\text{ }=\text{ }\mathbf{4}\text{ }\times \text{ }\mathbf{5}\]

\[\pm \text{ }\left( \mathbf{4a}\text{ }\text{ }\mathbf{12} \right)\text{ }=\text{ }\mathbf{20}\]

\[\mathbf{4a}\text{ }\text{ }\mathbf{12}\text{ }=\text{ }\mathbf{20}\text{ }\mathbf{or}\text{ }\text{ }\left( \mathbf{4a}\text{ }\text{ }\mathbf{12} \right)\text{ }=\text{ }\mathbf{20}\]

\[\mathbf{4a}\text{ }=\text{ }\mathbf{20}\text{ }+\text{ }\mathbf{12}\text{ }\mathbf{or}\text{ }\mathbf{4a}\text{ }=\text{ }-\text{ }\mathbf{20}\text{ }+\text{ }\mathbf{12}\]

\[\mathbf{a}\text{ }=\text{ }\mathbf{32}/\mathbf{4}\text{ }\mathbf{or}\text{ }\mathbf{a}\text{ }=\text{ }-\text{ }\mathbf{8}/\mathbf{4}\]

\[\mathbf{a}\text{ }=\text{ }\mathbf{8}\text{ }\mathbf{or}\text{ }\mathbf{a}\text{ }=\text{ }-\text{ }\mathbf{2}\]

∴ The necessary focuses on the x –axis are \[\left( -\text{ }\mathbf{2},\text{ }\mathbf{0} \right)\text{ }\mathbf{and}\text{ }\left( \mathbf{8},\text{ }\mathbf{0} \right)\]