# Q : 2     Find the values of  $\small \theta$ and $\small p$, if the equation  $\small x\cos \theta +y\sin \theta =p$ is the normal form of the line  $\small \sqrt{3}x+y+2=0$.

G Gautam harsolia

The normal form of the line is     $\small x\cos \theta +y\sin \theta =p$
Given the equation of lines is
$\small \sqrt{3}x+y+2=0$
First, we need to convert it into normal form. So, divide both the sides by $\small \sqrt{(\sqrt3)^2+1^2}= \sqrt{3+1}= \sqrt4=2$
$\small -\frac{\sqrt3\cos \theta}{2}-\frac{y}{2}= 1$
On comparing both
we will get
$\small \cos \theta = -\frac{\sqrt3}{2}, \sin \theta = -\frac{1}{2} \ and \ p = 1$
$\small \theta = \frac{7\pi}{6} \ and \ p =1$
Therefore, the answer is  $\small \theta = \frac{7\pi}{6} \ and \ p =1$

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