# Question #1a839

##### 1 Answer
Jan 13, 2018

Equation of line $A B$ is $y = 2$

#### Explanation:

$O \left(0 , 0\right)$ is the intersection point of the two given lines $\sqrt{3} x + y = 0 , \mathmr{and} \sqrt{3} x - y = 0$,
Given $y = \sqrt{3} x , s l o p e = \sqrt{3} , \implies \alpha = {\tan}^{-} 1 \sqrt{3} = {60}^{\circ}$
similarly, given $y = - \sqrt{3} x , \implies \beta = {60}^{\circ}$, as shown in the figure.
$\implies \angle A O B = 180 - 60 - 60 = {60}^{\circ}$
For $\Delta O A B$ to be equilateral, line $A B$ has to be parallel to the x-axis.
Hence, equation of line $A B$ that passes through $P \left(2 , 2\right)$ and is parallel to the x-axis is : $y = 2$