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

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.​

### 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. $$\textbf{Given:}$$

$$\textsf{Line is}$$

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

$$\textbf{To find:}$$

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

$$\textbf{Solution:}$$

$$\textsf{Consider,}$$

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

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

$$\textsf{Divide bothsides by 2}$$

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

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

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

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

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

$$\textbf{Find more:}$$

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

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