Question

The equation of the straight line which passes through $(1,1)$ and making angle ${60}^o$ with the line $x+\sqrt{3}y+2\sqrt{3}=0$ is/are.

• A. $y=1$
• B. $x=1$
• C. $x+y=2$
• D. $x+\sqrt{3}y-\sqrt{3}-1=0$

Answer 1

The correct option is B $x=1$

Let $m$ be slope of straight line.

Given, it makes ${60}^0$ with line $x+\sqrt{3}y+2\sqrt{3}=0$
We get, $\tan 60=\pm \left(\frac{-\frac{1}{\sqrt{3}}-m}{1-\frac{m}{\sqrt{3}}}\right)=\sqrt{3}$

Solving this, we get

$m=\frac{1}{\sqrt{3}}$ and $\frac{1}{m}=0$
$\therefore$ Equations of lines are

$\frac{y-1}{x-1}=\frac{1}{\sqrt{3}}$

$⟹x-\sqrt{3}y+\sqrt{3}-1=0$ and $x=1$