Question

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

• A. x-2=0
• B. $y-2=0$
• C. x + y - 4 = 0
• D. None of these

Answer 1

Answer: (B)

Given equations of lines are $\sqrt{3x}+y=0$ and $\sqrt{3x}-y=0$
The slopes of the lines are $\tan {\theta }_1=-\sqrt{3}$ and $\tan {\theta }_2=\sqrt{3}$ $\Rightarrow$ ${\theta }_1={120}^o$ and ${\theta }_2={60}^o$ Thus, the lines make angles $\text{12}0{}^{\circ }$ and $\text{6}0{}^{\circ }$ 1o the, X-axis. Any line parallel to X-axis forms an equilateral triangle and it passes through the point (2,2). Hence, equation of required line is y=2 or y-2=0,