Pair Of Straight Lines Question 135
Question: Two of the lines represented by the equation $ ay^{4}+bxy^{3}+cx^{2}y^{2}+dx^{3}y+ex^{4}=0 $ will be perpendicular, then
[Kurukshetra CEE 1998]
Options:
A) $ (b+d)(ad+be)+{{(e-a)}^{2}}(a+c+e)=0 $
B) $ (b+d)(ad+be)+{{(e+a)}^{2}}(a+c+e)=0 $
C) $ (b-d)(ad-be)+{{(e-a)}^{2}}(a+c+e)=0 $
D) $ (b-d)(ad-be)+{{(e+a)}^{2}}(a+c+e)=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ ay^{4}+bxy^{3}+cx^{2}y^{2}+dx^{3}y+ex^{4} $
$ =(ax^{2}+pxy-ay^{2})(x^{2}+qxy+y^{2}) $
Comparing the coefficient of similar terms. We get, $ b=aq-p,\ c=-pq $ , $ d=aq+p,\ e=-a $
$ b+d=2aq,\ e-a=-2a $
$ ad+be=2ap,a+c+e=-pq $
$ (b+d)(ad+be)=-{{(e-a)}^{2}}(a+c+e) $
$ (b+d)(ad+eb)+{{(e-a)}^{2}}(a+c+e)=0 $ .
BETA
