Pair Of Straight Lines Question 44
Question: If the sum of slopes of the pair of lines represented by $ 4x^{2}+2hxy-7y^{2}=0 $ is equal to the product of the slopes, then the value of $ h $ is
[Karnataka CET 1999]
Options:
A) - 6
B) - 2
C) - 4
D) 4
Show Answer
Answer:
Correct Answer: B
Solution:
Comparing the given equation with the standard equation, we get $ a=4 $ and $ b=-7 $ . Let $ m_1 $ and $ m_2 $ are the slopes of given lines.
Therefore sum of the slopes $ (m_1+m_2)=-\frac{2h}{b}=\frac{2h}{7} $ and product of the slopes $ (m_1m_2)=\frac{a}{b}=\frac{4}{-7} $ . $ \because m_1+m_2=m_1m_2 $ , therefore $ \frac{2h}{7}=\frac{4}{-7} $ or $ h=-2 $ .
BETA
