Pair Of Straight Lines Question 1
Question: If the lines represented by the equation $ ax^{2}-bxy-y^{2}=0 $ make angles $ \alpha $ and $ \beta $ with the x-axis, then $ \tan (\alpha +\beta ) $ =
Options:
A) $ \frac{b}{1+a} $ .
B) $ \frac{-b}{1+a} $
C) $ \frac{a}{1+b} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Here the equation is $ ax^{2}-bxy-y^{2}=0 $ and given that $ m_1=\tan \alpha $ and $ m_2=\tan \beta $
and we know that $ m_1+m_2=\frac{b}{-1}=\tan \alpha +\tan \beta $ and $ m_1m_2=\frac{a}{-1}=\tan \alpha .\tan \beta $
$ \tan (\alpha +\beta )=\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=\frac{-b}{1-(-a)}=\frac{-b}{(1+a)} $ .
BETA
