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Mathematics

Coordinate-Geometry

Easy

Question

$A space s t r a i g h t space l i n e space L space a t space a space d i s tan c e space o f space 4 space u n i t s space f r o m space t h e space o r i g i n space m a k e s space p o s i t i v e space i n t e r c e p t s space o n space t h e space c o o r d i n a t e space a x e s space a n d space t h e space p e r p e n d i c u l a r space f r o m space t h e space o r i g i n space t o space t h i s space l i n e space m a k e s space a n space a n g l e space o f space 60 º space w i t h space t h e space l i n e space x space plus space y space equals space 0. space T h e n space a n space e q u a t i o n space o f space t h e space l i n e space L space i s space colon$

$x + \sqrt{3} y = 8$
$(\sqrt{3} - 1) x + (\sqrt{3} + 1) y = 8 \sqrt{2}$
$(\sqrt{3} + 1) x + (\sqrt{3} - 1) y = 8 \sqrt{2}$
$\sqrt{3} x + y = 8$

The correct answers are: $left parenthesis square root of 3 plus 1 right parenthesis x plus left parenthesis square root of 3 minus 1 right parenthesis y equals 8 square root of 2$ , $left parenthesis square root of 3 minus 1 right parenthesis x plus left parenthesis square root of 3 plus 1 right parenthesis y equals 8 square root of 2$

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$text Lines are drawn parallel to the line end text 4 x minus 3 y plus 2 equals 0 comma text at a distance end text 3 over 5 text from the origin. Then which one of the end text f o l l o w i n g space p o i n t s space l i e s space o n space a n y space o f space t h e s e space l i n e s space ?$

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