Question

What is the equation of the straight line cutting off an intercept $2$ from the negative direction of y-axis and inclined at ${30}^o$ with the positive direction of x-axis?

• A. $x-\sqrt{3}y-2\sqrt{3}=0$
• B. $x+2\sqrt{3}y-3\sqrt{2}=0$
• C. $x-2\sqrt{3}y+3\sqrt{2}=0$
• D. $x-2\sqrt{3}y-2\sqrt{3}=0$

Answer 1

The correct option is A $x-\sqrt{3}y-2\sqrt{3}=0$

Inclined at ${30}^{\circ }$ with positive X-axis

$\tan \theta =\tan {30}^{\circ }=\frac{1}{\sqrt{3}}=Slope$

$\therefore y=mx+c$..........(i)

$y$ intercept $=-2$

$\therefore$ put $x=0$

$c=-2$.........from (i)

$\therefore$ Equation $y=\frac{x}{\sqrt{3}}-2$

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