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  • Find the values of θ and p, if the equation x cos θ + y sinθ = p is the normal form of the line sqrt 3 x + y + 2 = 0.

 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.

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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

Posted by

Gautam harsolia

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