Given:
![\[p\text{ }=\text{ }4,\text{ }\alpha \text{ }=\text{ }30{}^\circ \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b506d1a464ad004afb2bffba52b0d7ac_l3.png "Rendered by QuickLaTeX.com")
The equation of the line in normal form is given by
On using the formula,
![\[x\text{ }cos~\alpha \text{ }+\text{ }y\text{ }sin\text{ }\alpha \text{ }=\text{ }p\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-46b724860300ac9f5afca091b543b42b_l3.png "Rendered by QuickLaTeX.com")
Now, putting the values, we get
![\[x\text{ }cos\text{ }30{}^\circ \text{ }+\text{ }y\text{ }sin\text{ }30{}^\circ \text{ }=\text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3c6ccf9b5e8d2db549dde09e13dee831_l3.png "Rendered by QuickLaTeX.com")
![\[x\surd 3/2\text{ }+\text{ }y1/2\text{ }=\text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e9e384160863b28fb0a927fdd813aca8_l3.png "Rendered by QuickLaTeX.com")
![\[\surd 3x\text{ }+\text{ }y\text{ }=\text{ }8\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-566b1ec5b0b2bfb9d26c8ad946ad734f_l3.png "Rendered by QuickLaTeX.com")
∴ The equation of line in normal form is:
![\[~\surd 3x\text{ }+\text{ }y\text{ }=\text{ }8.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-58e7f34f84b4ad00ec6385a8e18f1a9a_l3.png "Rendered by QuickLaTeX.com")
Find the equation of the line on which the length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x–axis is 30°.
Find the equation of the line on which the length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x–axis is 30°.