Convert straight line √3 x – y + 2 = 0in perpendicular form. Find the length of perpendicular from origin to the line and also the

1 thought on “Convert straight line √3 x – y + 2 = 0in perpendicular form. Find the length of perpendicular from origin to the line and also the”

1. [tex]\textbf{Given:}[/tex]

   [tex]\textsf{Line is}[/tex]

   [tex]\mathsf{\sqrt{3}x-y+2=0}[/tex]

   [tex]\textbf{To find:}[/tex]

   [tex]\textsf{Perpendiclar form of the given line}[/tex]

   [tex]\textbf{Solution:}[/tex]

   [tex]\textsf{Consider,}[/tex]

   [tex]\mathsf{\sqrt{3}x-y+2=0}[/tex]

   [tex]\mathsf{\sqrt{3}x-y=-2}[/tex]

   [tex]\textsf{Divide bothsides by 2}[/tex]

   [tex]\mathsf{\dfrac{\sqrt{3}}{2}x-\dfrac{1}{2}y=-1}[/tex]

   [tex]\mathsf{x\left(\dfrac{-\sqrt{3}}{2}\right)+y\left(\dfrac{1}{2}\right)=1}[/tex]

   [tex]\mathsf{x\,cos\left(\dfrac{5\pi}{6}\right)+y\,sin\left(\dfrac{5\pi}{6}\right)=1}[/tex]

   [tex]\mathsf{Comparing\,with\;x\,cos\alpha+y\,sin\alpha=p\;we\;get}[/tex]

   [tex]\mathsf{\alpha=\dfrac{5\pi}{6}\;\;and\;\;p=1}[/tex]

   [tex]\textbf{Find more:}[/tex]

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

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