Pair Of Straight Lines Question 30
Question: The condition of representing the coincident lines by the general quadratic equation $ f(x,y)=0 $ , is
Options:
A) $ \Delta =0 $ and $ h^{2}=ab $
B) $ \Delta =0 $ and $ a+b=0 $
C) $ \Delta =0 $ and $ h^{2}=ab $ , $ g^{2}=ac $ , $ f^{2}=bc $
D) $ h^{2}=ab $ , $ g^{2}=ac $ and $ f^{2}=bc $
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Answer:
Correct Answer: B , C
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
