Question

Equation to the straight line cutting off an intercept $2$ from the negative direction of the axis of $y$ and inclined at $30°$ to the positive direction of axis of$x$, is

• A. $y+x–\surd 3=0$
• B. $y–x+2=0$
• C. $y–\surd 3x–2=0$
• D. $\surd 3y–x+2\surd 3=0$

Answer 1

The correct option is D

$\surd 3y–x+2\surd 3=0$

Given, $\theta =30°$

$\therefore$Slope $=\tan 30°$

$=\frac{1}{\surd 3}$

Also, Y-intercept is $-2$

$\Rightarrow$It passes through $(0,-2)$

$\therefore$The required equation of the line is

$y–y_1=m(x–x_1)$

$\Rightarrow$ $y+2=\frac{1}{\surd 3}(x–0)$

$\Rightarrow$$\surd 3y+2\surd 3–x=0$

Hence, Option ‘D’ is Correct.