Pair Of Straight Lines Question 141
Question: If the equation $ ax^{2}+2hxy+by^{2}=0 $ has the one line as the bisector of angle between the coordinate axes, then
[Bihar CEE 1990]
Options:
A) $ {{(a-b)}^{2}}=h^{2} $
B) $ {{(a+b)}^{2}}=h^{2} $
C) $ {{(a-b)}^{2}}=4h^{2} $
D) $ {{(a+b)}^{2}}=4h^{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
Let one line be $ x+y=0\Rightarrow m_1=-1 $ and we know that $ m_1+m_2=-\frac{2h}{b} $ …..(i) and $ m_1m_2=\frac{a}{b} $ …..(ii)
Therefore from (ii), $ m_2=-\frac{a}{b} $
$ \Rightarrow -1-\frac{a}{b}=\frac{-2h}{b}\Rightarrow {{(a+b)}^{2}}=4h^{2} $ .
BETA
