Pair Of Straight Lines Question 6
Question: If $ 4ab=3h^{2} $ , then the ratio of slopes of the lines represented by the equation $ ax^{2}+2hxy+by^{2}=0 $ will be
Options:
A) $ \sqrt{2}:1 $
B) $ \sqrt{3}:1 $
C) $ 2:1 $
D) $ 1:3 $
Show Answer
Answer:
Correct Answer: D
Solution:
Here $ m_1+m_2=\frac{-2h}{b} $ …..(i)
and $ m_1m_2=\frac{a}{b} $ …..(ii)
Also, given that $ 4ab=3h^{2}. $
Now we have to find $ \frac{m_1}{m_2} $ ,
therefore with the help of (i) and (ii), we get
$ {{(m_1-m_2)}^{2}}=\frac{4h^{2}-4ab}{b^{2}}=\frac{4h^{2}-3h^{2}}{b^{2}}=\frac{h^{2}}{b^{2}} $
Therefore $ m_1-m_2=\frac{h}{b} $ …..(iii) Now on solving (i) and (iii), we get $ m_1=\frac{-h}{2b} $
and $ m_2=\frac{-3h}{2b} $ ;
$ m_1:m_2=1:3 $ .
BETA
