Question

A straight line through $(2,2)$ intersect the lines, $y+x\sqrt{3}=0$ and $y-x\sqrt{3}=0$ at $A$ and $B$. If $OAB$ (where $O$ is the origin) is an equilateral triangle, then the equation of $AB$ is

• A. $x-2=0$
• B. $y-2=0$
• C. $x-y=0$
• D. $x+y-4=0$

Answer 1

The correct option is B $y-2=0$

$y=x\sqrt{3}$ has a slope $\sqrt{3}$ and is inclined at ${60}^0$ to the x-axis i.e $OX$

and $y=-x\sqrt{3}$ is inclined at ${60}^0$ to $O{X}^{\prime }$

$\angle AOY=\angle BOY={30}^0$ since, $OY$ is equally inclined to $OA$ and $OB$, $AB$ must be parallel to x-axis and also passes through $(2,2)$

Hence equation of $AB$(through $P$) is $y=2$