![\[\left( \mathbf{i} \right)\text{ }\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }\text{ }\mathbf{34}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }+\text{ }\mathbf{31}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-cd7250d7566f1da5db8c6a98939037a0_l3.png "Rendered by QuickLaTeX.com")
Given:
The equal lines are
![\[\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }\text{ }\mathbf{34}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{15x}\text{ }+\text{ }\mathbf{8y}\text{ }+\text{ }\mathbf{31}\text{ }=\text{ }\mathbf{0}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6b3df176ce568b147ddc61537ffa7000_l3.png "Rendered by QuickLaTeX.com")
By utilizing the equation,
The distance (d) between equal lines
![\[\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C1}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-49f588c33b6e02448dc5477342e3ee1e_l3.png "Rendered by QuickLaTeX.com")
and
![\[\mathbf{Ax}\text{ }+\text{ }\mathbf{By}\text{ }+\text{ }\mathbf{C2}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-22f7fb4b371a1433191fbcec9d88f0b1_l3.png "Rendered by QuickLaTeX.com")
is given by
∴ The distance between equal lines is
![\[\mathbf{65}/\mathbf{17}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7dba07f7155b1a4162e2ae462dd3ea04_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{ii} \right)\text{ }\mathbf{l}\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }+\text{ }\mathbf{p}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{l}\text{ }\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }\text{ }\mathbf{r}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dd59e8d636e46191a8f2849e168b4d1f_l3.png "Rendered by QuickLaTeX.com")
Given:
The equal lines are
![\[\mathbf{l}\text{ }\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }+\text{ }\mathbf{p}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{l}\text{ }\left( \mathbf{x}\text{ }+\text{ }\mathbf{y} \right)\text{ }\text{ }\mathbf{r}\text{ }=\text{ }\mathbf{0}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-761a40422cf6b3983f1b5f7fba90c3c7_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{lx}\text{ }+\text{ }\mathbf{ly}\text{ }+\text{ }\mathbf{p}\text{ }=\text{ }\mathbf{0}\text{ }\mathbf{and}\text{ }\mathbf{lx}\text{ }+\text{ }\mathbf{ly}\text{ }\text{ }\mathbf{r}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-74a19864070498d655becd348dcc04e7_l3.png "Rendered by QuickLaTeX.com")
by utilizing the equation,
The distance (d) between equal lines
and
is given by
∴ The distance between equal lines is
![\[\left| \mathbf{p}+\mathbf{r} \right|/\mathbf{l}\surd \mathbf{2}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d2c92e2e49c0b6842fc5cc1e6da2576a_l3.png "Rendered by QuickLaTeX.com")
