\[\left( \mathbf{iii} \right)\text{ }\mathbf{x-}\text{ }\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{4}\]

Given:

The condition is \[\mathbf{x-}\text{ }\text{ }\mathbf{y}\text{ }+\text{ }\mathbf{4}\text{ }=\text{ }\mathbf{0}\]

Condition of line in ordinary structure is given by \[\mathbf{x-}\text{ }\mathbf{cos}\text{ }\mathbf{\theta }\text{ }+\text{ }\mathbf{y}\text{ }\mathbf{sin}\text{ }\mathbf{\theta }\text{ }=\text{ }\mathbf{p}\] where ‘θ’ is the point among opposite and positive x hub and ‘p’ is opposite separation from beginning.

So presently, \[\mathbf{x}\text{ }\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{4}\]

Gap both the sides by \[\surd \left( \mathbf{12}\text{ }+\text{ }\mathbf{12} \right)\text{ }=\text{ }\surd \left( \mathbf{1}+\mathbf{1} \right)\text{ }=\text{ }\surd \mathbf{2}\]

\[\mathbf{x}/\surd \mathbf{2}\text{ }\text{ }\mathbf{y}/\surd \mathbf{2}\text{ }=\text{ }\mathbf{4}/\surd \mathbf{2}\]

\[\left( \mathbf{1}/\surd \mathbf{2} \right)\mathbf{x}\text{ }+\text{ }\left( -\text{ }\mathbf{1}/\surd \mathbf{2} \right)\mathbf{y}\text{ }=\text{ }\mathbf{2}\surd \mathbf{2}\]

This is in the structure: \[\mathbf{x}\text{ }\mathbf{cos}\text{ }\mathbf{315o}\text{ }+\text{ }\mathbf{y}\text{ }\mathbf{sin}\text{ }\mathbf{315o}\text{ }=\text{ }\mathbf{2}\surd \mathbf{2}\]

∴ The above condition is of the structure\[\mathbf{x}\text{ }\mathbf{cos}\text{ }\mathbf{\theta }\text{ }+\text{ }\mathbf{y}\text{ }\mathbf{sin}\text{ }\mathbf{\theta }\text{ }=\text{ }\mathbf{p}\] , where \[\mathbf{\theta }\text{ }=\text{ }\mathbf{315}{}^\circ \] and \[\mathbf{p}\text{ }=\text{ }\mathbf{2}\surd \mathbf{2}.\]

Opposite distance of line from beginning \[=\text{ }\mathbf{2}\surd \mathbf{2}\]

Point among opposite and positive x – axis \[=\text{ }\mathbf{315}{}^\circ \]