Pair Of Straight Lines Question 62
Question: If $ \frac{x^{2}}{a}+\frac{y^{2}}{b}+\frac{2xy}{h}=0 $ represent pair of straight lines and slope of one line is twice the other. Then $ ab:h^{2} $ is
[DCE 2005]
Options:
A) 9 : 8
B) 8 : 9
C) 1 : 2
D) 2 : 1
Show Answer
Answer:
Correct Answer: A
Solution:
Let $ m_1,m_2 $ be the slopes
$ \therefore $ $ m_1+m_2=-\frac{2b}{h} $ and $ m_1m_2=\frac{b}{a} $
Again $ m_2 $ = $ 2m_1 $
$ \therefore $ $ 3m_1=-\frac{2b}{h} $ and $ 2m_1^{2}=\frac{b}{a} $
$ \therefore $ $ \frac{9m_1^{2}}{2m_1^{2}}=\frac{4b^{2}}{h^{2}}\times \frac{a}{b}\Rightarrow ab:h^{2}=9:8 $ .
BETA
