First slide

Pair of straight lines

Question

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

Moderate

A

$\sqrt{3} x^{2} - x y = 0$
B

$\sqrt{3} x^{2} + x y = 0$
C

$\sqrt{3} x^{2} - x = 0$
D

$\sqrt{3} x^{2} - y = 0$

Solution

$E q u a t i o n s o f t h e g i v e n l i n e s a r e y = \sqrt{3} x, y = \frac{1}{\sqrt{3}} x T h e s e t w o l i n e s c a n b e w r i t t e n a s y = \tan 60^{\circ} x a n d y = \tan 30^{\circ} x A f t e r r o t a t i o n t h e e q u a t i o n s b e c o m e s y = \tan 90^{\circ} x a n d y = \tan 60^{\circ} x E q u a t i o n s a r e x = 0, a n d y = \sqrt{3} x T h e c o m b i n e d e q u a t i o n i s \sqrt{3} x^{2} - x y = 0$

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