Question

Convert straight line √3 x - y + 2 = 0in perpendicular form. Find the length of perpendicular from origin to the line and also the angle made by perpendicular with x-axis.​

Answer 1

$\textbf{Given:}$

$\textsf{Line is}$

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

$\textbf{To find:}$

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

$\textbf{Solution:}$

$\textsf{Consider,}$

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

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

$\textsf{Divide bothsides by 2}$

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

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

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

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

$\mathsf{\alpha=\dfrac{5\pi}{6}\;\;and\;\;p=1}$

$\textbf{Find more:}$

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

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