First slide

Pair of straight lines

Question

$T w o p a i r s o f l i n e s 2 x^{2} + 6 x y + y^{2} = 0 a n d 4 x^{2} + 18 x y + y^{2} = 0$

Moderate

A

one is angular bisector of the other
B

not equally inclined
C

both posses same angular bisectors
D

one is the angular bisector of the coordinate axes

Solution

$T h e a n g u l a r b i s e c t o r o f a x^{2} + 2 h x y + b y^{2} = 0 i s h (x^{2} - y^{2}) - x y (a - b) = 0$
$T h e a n g u l a r b i s e c t o r o f 2 x^{2} + 6 x y + y^{2} = 0 i s 3 x^{2} - x y - 3 y^{2} = 0$
$T h e a n g u l a r b i s e c t o r o f 4 x^{2} + 18 x y + y^{2} = 0 i s 9 x^{2} - 3 x y - 9 y^{2} = 0$
$T h e a b o v e t w o e q u a t i o n s r e p r e s e n t s s a m e s e t o f p a i r o f l i n e s$
$i t m e a n s b o t h t h e p a i r o f l i n e s p o s s e s s s a m e a n g u a l r b i s e c t o r s$

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