Question

A straight line through the point $(2,2)$ intersects the lines $\sqrt{3}x+y=0$ and $\sqrt{3}x-y=0$ at the point $A$ and $B.$ The equation to the line $AB$ so that the triangle $OAB$ is equilateral is

Answer 1

Let, that O is the origin. and I think the question should read as what is the equation of line AB so (or such) that the triangle ΔAOB is equilateral.
Given $y=\surd 3x$,slope$=\surd 3$,⇒α=tan−1√3=60∘
similarly, as $y$=−√3x,⇒β=60∘, as shown in the figure.
⇒∠BOA=180−60−60=60^o
For ΔOAB to be equilateral, line AB has to be parallel to the $x$-axis.
Hence, equation of line AB that passes through $P(2,2)$and is parallel to the $x$-axis is :$y=2$