Question

Reduce the equation √3x-y-2 = 0 into normal form. Find the values of p and a
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Answer 1

$\textbf{Given:}$

$\textsf{Line is}$

$\mathsf{\sqrt{3}x-y-2=0}$

$\textbf{To find:}$

$\textsf{Normal form of the given line}$

$\mathsf{}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\sqrt{3}x-y-2=0}$

$\mathsf{\sqrt{3}x-y=2}$

$\textsf{Divide bothsides by 2}$

$\mathsf{\dfrac{\sqrt{3}}{2}x-\dfrac{1}{2}y=1}$

$\mathsf{x\left(\dfrac{\sqrt{3}}{2}\right)+y\left(\dfrac{-1}{2}\right)=1}$

$\mathsf{x\,cos\left(\dfrac{-\pi}{6}\right)+y\,sin\left(\dfrac{-\pi}{6}\right)=1}$

$\mathsf{Comparing\,with\;x\,cos\alpha+y\,sin\alpha=p\;we\;get}$

$\mathsf{\alpha=\dfrac{-\pi}{6}\;\;and\;\;p=1}$

$\textbf{Find more:}$

Reduce the equation root 3x+y+2=0 to 1)slope intercept form 2)intercept form and 3) normal form

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