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$T h e c o m b i n e d e q u a t i o n o f p a i r o f l i n e s i s \sqrt{3} x^{2} - 4 x y + \sqrt{3} y^{2} = 0, i f t h e l i n e s w e r e r o t a t e d a b o u t t h e o r i g i n b y \frac{π}{6} i n t h e a n t i c l o c k w i s e d i r e c t i o n t h e n t h e n e w p o s i t i o n i s$

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3x2-xy=0

3x2+xy=0

3x2-x=0

3x2-y=0

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Correct option is A

Equations of the given lines are y=3x,y=13x These two lines can be written as y=tan 60∘x and y=tan30∘x After rotation the equations becomes y=tan90∘x and y=tan 60∘x Equations are x=0, and y=3x The combined equation is 3x2-xy=0

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The combined equation of pair of lines is 3x2-4xy+3y2=0, if the lines were rotated about the origin by π6 in the anticlock wise direction then the new position is

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$T h e c o m b i n e d e q u a t i o n o f p a i r o f l i n e s i s \sqrt{3} x^{2} - 4 x y + \sqrt{3} y^{2} = 0, i f t h e l i n e s w e r e r o t a t e d a b o u t t h e o r i g i n b y \frac{π}{6} i n t h e a n t i c l o c k w i s e d i r e c t i o n t h e n t h e n e w p o s i t i o n i s$