If the pair of lines x 2 − 16 p x y − y 2 = 0 and x 2 − 16 q x y − y 2 = 0 are such that each pair bisects the angle between the other pair, then pq =

Question

If the pair of lines x 2 − 16 p x y − y 2 = 0 and x 2 − 16 q x y − y 2 = 0 are such that each pair bisects the angle between the other pair, then pq =, 64 − 1 ​, 64 1 ​, 8 − 1 ​, 8 1 ​

MARKS App · Accepted Answer

We have, equations of pair of straight lines Now, equations of bisectors of these line are $ − 8 p x 2 − 2 x y + 8 p y 2 = 0 im g src = " h ttp s : // c d n − q u es t i o n − p oo l . g e t ma r k s . a pp / p y q / a p e ​ am ce t /3 f Y r 1 KDsH j t h v 99 v 48 − Xtl b t h 6 Q 4 p s T Vm 1 H U 5 i e m U w o . or i g ina l . f u ll s i ze . p n g " > b r > an d -8 q x^2-2 x y+8 q y^2=0 im g src = " h ttp s : // c d n − q u es t i o n − p oo l . g e t ma r k s . a pp / p y q / a p e ​ am ce t / x D L − f A v M f u 9 z B d G f e C o b I w c t U ​ V 0 z R r i u j H B ​ m o x e MQ . or i g ina l . f u ll s i ze . p n g " > b r > A ccor d in g t o t h e g i v e n co n d i t i o nin t h e d a t a , Eq s . ( i ) an d ( i v ) , an d Eq s . ( ii ) an d ( iii ) m u s t b eco in c i d e n t . S o , 4 q 1 ​ = 1 − 16 p ​ = − 4 q − 1 ​ 1 = − 64 pq ∴ pq = 64 − 1 ​ ​ $

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