Pair Of Straight Lines Question 45
Question: The gradient of one of the lines of $ ax^{2}+2hxy+by^{2}=0 $ is twice that of the other, then
[MP PET 2000; Pb. CET 2002]
Options:
A) $ h^{2}=ab $
B) $ h=a+b $
C) $ 8h^{2}=9ab $
D) $ 9h^{2}=8ab $
Show Answer
Answer:
Correct Answer: C
Solution:
Here, $ m_1+m_2=\frac{-2h}{b} $ and $ m_1m_2=\frac{a}{b} $ Given that $ m_1=2m_2 $
$ \therefore $ $ 3m_2=\frac{-2h}{b} $ and $ 2m_2^{2}=\frac{a}{b} $
Therefore $ 2{{( \frac{-2h}{3b} )}^{2}}=\frac{a}{b} $
Therefore $ 8h^{2}=9ab $ .
BETA
