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  4. The length of the perpendicular from the origin to a line is 7 and line makes an angle of 150° with the positive direction of y -axis then the equation of the line is

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Q. The length of the perpendicular from the origin to a line is $7$ and line makes an angle of $150^{\circ}$ with the positive direction of $y$ -axis then the equation of the line is

Straight Lines

Solution:

Here $p = 7$ and $\alpha = 30^{\circ}$
image
$\therefore $ Equation of the required line is
$x \cos 30^{\circ}+y \sin 30^{\circ}=7$
or $\times \frac{\sqrt{3}}{2}+y \times \frac{1}{2}=7$ or
$\sqrt{3} x+y=14$