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


A) \( \Large x-2=0 \)

B) \( \Large y-2=0 \)

C) \( \Large x+y-4=0 \)

D) none of these

Correct Answer:
B) \( \Large y-2=0 \)

Description for Correct answer:

From the given equations, we get

\( \Large m^{2}+am+2=0 \)

Since, m is real \( \Large a^{2}\ge 8,\ |a| \ge 2\sqrt{2} \)

So least value of \( \Large |a|\ is\ 2\sqrt{2} \)

\( \Large \sqrt{3}x+y=0 \) makes an angle of \( \Large 120 ^{\circ} \) with OX and \( \Large \sqrt{3}x-y=0 \) makes an angle \( \Large 60 ^{\circ} \) with OX.

So the required line is \( \Large y-2=0 \)

Part of solved Straight lines questions and answers : >> Elementary Mathematics >> Straight lines




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