Pair Of Straight Lines Question 88
Question: If the slope of one of the lines given by $ ax^{2}+2hxy+by^{2}=0 $ is 5 times the other, then
[Karnataka CET 2003]
Options:
A) $ 5h^{2}=ab $
B) $ 5h^{2}=9ab $
C) $ 9h^{2}=5ab $
D) $ h^{2}=ab $
Show Answer
Answer:
Correct Answer: B
Solution:
Given $ m_2=5m_1\Rightarrow m_1+5m_1=\frac{-2h}{b} $
Therefore $ m_1=\frac{-2h}{6b} $ …(i) and $ m_1.5m_1=\frac{a}{b}\Rightarrow m_1=\sqrt{\frac{a}{5b}} $ …(ii) From (i) and (ii), $ \frac{-2h}{6b}=\sqrt{\frac{a}{5b}} $
Therefore $ \frac{4h^{2}}{36b^{2}}=\frac{a}{5b} $
Therefore $ 9ab=5h^{2} $ .
BETA
