A straight line through (2,2) intersects lines (√3)x+y=0 and (√3)x−y=0 at pts. A & B respectively. Find equation of line AB so that ΔOAB is equilateral?


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Question Number 47457 by rahul 19 last updated on 10/Nov/18

$A s t r a i g h t l i n e t h r o u g h (2, 2) i n t e r s e c t s$ $l i n e s \sqrt{3} x + y = 0 a n d \sqrt{3} x - y = 0 a t p t s .$ $A & B r e s p e c t i v e l y . F i n d e q u a t i o n$ $o f l i n e A B s o t h a t Δ O A B i s e q u i l a t e r a l ?$
	Answered by rahul 19 last updated on 10/Nov/18

	$\sqrt{3} x + y = 0 m a k e s a n a n g l e o f 120 ° w i t h$ $O X w h e r e a s \sqrt{3} x - y = 0 m a k e s a n a n g l e$ $o f 60 ° w i t h O X .$ $∴ r e q u i r e d l i n e i s y = 2 .$
	Commented byrahul 19 last updated on 10/Nov/18

	$o k, s i r . .$
	Commented byrahul 19 last updated on 10/Nov/18

	$t h i s i s h i n t g i v e n . . . .$ $I w a n t t o k n o w w h e t h e r a n y o t h e r$ $l i n e s a t i s f i e s t h e c o n d i t i o n o r i s i t$ $u n i q u e ?$
	Commented bymr W last updated on 10/Nov/18

	$y = 2 i s t h e u n i q u e s o l u t i o n .$
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